禾略算法应用分享——股市因子回测&疫情元胞机

<p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;"><span style="display: none;line-height: 0px;"><span style="display: none;line-height: 0px;">‍</span>‍</span>一场突如其来的疫情导致房地产市场前景并不明朗，大家纷纷前往股市“赌博”，这次90后算命大师带来分享——<span style="font-family: 微软雅黑;font-size: 14px;">股市行业基本面因子回测和疫情元胞机</span>，解释数据如何让世界更理性，希望大家不吝赐教。<br /><br /></span></p><p style="text-align: left;margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 24px;"><strong><span style="font-size: 24px;font-family: 微软雅黑;font-weight: bold;">NO.</span></strong><strong><span style="font-size: 24px;font-family: 微软雅黑;font-weight: bold;">1</span></strong></span></p><p style="text-align: left;margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 18px;"><strong><span style="font-size: 18px;font-family: 微软雅黑;font-weight: bold;">股市行业基本面因子回测</span></strong></span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">新冠疫情冲击全球股市，2020年3月美股四次熔断，“见证历史”成了每个普通人放在嘴边的高频词汇。<span style="font-family: 微软雅黑;">近期，A股也进入忽高忽低的过山车模式</span>，多数股票投资者是否有很多问号？<br /></span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;color: rgb(2, 30, 170);"><strong><br /></strong></span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;color: rgb(2, 30, 170);"><strong>如何才能进场获利？</strong></span><span style="font-family: 微软雅黑;font-size: 14px;">我们借鉴金融市场中证券的定价模型，解释了不同股票的收益率差异可以用哪些因子反映。<br /><br /></span></p><p style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMBfjFxoKYiaJG2W3a5y1FiazfZf0ibLcCHCsEtZDiaBRibU5USiavT0J7HsibQ/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></p><p style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><strong>首先对单个金融资产的收益率进行分解</strong>，按照资产所承担的风险分为无风险收益与风险收益，无风险收益资产例如国债等，因有国家主权担保所以风险很小，相应收益也很小，风险资产由于承担了更大的风险，所以需要更高的风险溢价进行补偿，收益率是这种风险溢价的体现。</span><br /></p><p style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><br /></span></p><p style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><strong>进一步对风险收益进行分解，</strong>美国人做出了三种模型解释，Sharp1964年的单因子模型将个股收益率与整体市场风险联系起来，Fama1993年的三因子模型，加入了市净率风险与规模风险</span><span style="font-family: 微软雅黑;font-size: 14px;">。举个例子，小公司应当具备更大的风险溢价，我们通常把市场风险收益即大盘大势收益称为<span style="font-family: 微软雅黑;font-size: 14px;">β</span>收益，<span style="font-family: 微软雅黑;font-size: 14px;">β</span>之上的超额部分成为<span style="font-family: 微软雅黑;font-size: 14px;"><span style="font-family: 微软雅黑;font-size: 14px;"></span>α</span>收益。</span></p><p style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><br /></span></p><p style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><span style="font-family: 微软雅黑;font-size: 14px;"><strong>“价值发现过程即超额收益消失过程”</strong>，</span>α与β收益之间其实是有一种动态的辩证关系，并不是一成不变的，随着越来越多人发现了<span style="font-family: 微软雅黑;font-size: 14px;">α</span>收益，他们的一致性操作会使得本来的<span style="font-family: 微软雅黑;font-size: 14px;">α</span>超额收益逐渐变为<span style="font-family: 微软雅黑;font-size: 14px;">β</span>整体市场收益。这可能就是巴菲特为什么会劝一般投资者购买股票指数而非个股，因为在长期来看，抓住<span style="font-family: 微软雅黑;font-size: 14px;">α</span>超额利润对于一般投资者来说并不简单。<br /></span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;"><br /></span></p><p style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">我们了解了市场收益的原理后，</span><span style="font-family: 微软雅黑;font-size: 14px;color: rgb(2, 30, 170);"><strong>如何找到一些能够影响收益的有效因子，同时如何验证这些因子是不是真实有效的呢？</strong></span><br /></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;<br /></span></p><p style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMOmiaKGYia6CPaWrUiaLebRicXPjxtp42DjZP5Nb6DqlsiboQicRHqZUMjPOw/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /></p><p style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"></span><br /><span style="font-family: 微软雅黑;font-size: 14px;"></span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">下面我们来讲下因子收益回测模拟的框架思路——<br />我们需要在历史数据中进行</span><span style="font-family: 微软雅黑;font-size: 14px;color: rgb(2, 30, 170);"><strong>回测</strong></span><span style="font-family: 微软雅黑;font-size: 14px;">，回测顾名思义就是假设我们回到过去的场景中，用这个因子进行投资标的的选择，我们的收益率表现会如何？跑赢大盘or跑输大盘，如果跑赢较多，就能够在一定程度上证明因子的有效性。<br /><br /></span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">具体方法简单来说，将过去的时间分解为相等长度的持仓周期，如上图所示：期初t0时间使用因子挑选投资标的称为调仓，之后每经过m个单位时间的持仓周期，再进行下一次调仓，在每一个持仓的时间段进行收益率的累计统计，最终把各个持仓时间的收益率累计起来，就可以得到基于这个因子的投资策略回测期收益表现。<br /><br /></span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">这其中一定要<strong>注意区分过去与未来信息</strong>。在每一个调仓/换仓时点，就是我们在选择资产标的的时候，一定要保证仅利用在这个时点可以知道的过去信息，不可以把未来才能知道的信息特别是未来标的收益率的信息用来调仓，这相当于提前知道了正确答案，相当于作弊，一般称这种情况为<strong>“信息泄露”</strong>或<strong>“引入了未来函数”</strong>，在这种情况下的回测结果可能出现虚假的高收益，但这是不可信的。</span></p><p style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;<br /></span></p><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMZJx4EDbzFGKHq7zAKfPD1fheicKS81G7YIVuNgCzoDN3MTNwJqaichTA/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;"><br />再进一步我们用一个具体案例来讲一下回测过程，</span><span style="font-family: 微软雅黑;font-size: 14px;color: rgb(2, 30, 170);"><strong>假设我们认为这两个因子：净资产成长因子（资产收益率）+估值因子（市销率），是比较有效的选股因子，</strong><strong>该如何验证因子的有效性？<br /><br /></strong></span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">我们按时间把投资过程分为两期：<strong>期初和期</strong></span><span style="font-family: 微软雅黑;font-size: 14px;"><strong>末，以沪深300作为股票池进行回测</strong></span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><strong><span style="font-family: 微软雅黑;font-size: 14px;">【期初】</span></strong><span style="font-family: 微软雅黑;font-size: 14px;">做因子排序选股，把股票池里的股票先按照第一因子从高到低排序，之后分位五个等分，之后的每个等分再用第二因子市销率倒数高低排序，选取前25%股票，这样形成5个分位的投资组合。<br /></span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><strong><span style="font-family: 微软雅黑;font-size: 14px;">【期末】</span></strong><span style="font-family: 微软雅黑;font-size: 14px;">对5个投资组合的收益表现进行统计，检验投资收益，如果期初的因子排序与期末的收益率排序具有较强相关</span><span style="font-family: 微软雅黑;font-size: 14px;">性，我们就说因子是有效的。<br /><br /></span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">上图是我们对2017-2019年沪深三百股票池滚动回测的因子净值收益表现（净值就是回答期初的1块钱，期末可以变成多少钱<span style="font-family: 微软雅黑;font-size: 14px;">）</span>。可以发现最好因子分位股票对应着最好的收益率，最差因子分位对应着最差的收益率，市场收益率即大盘收益被夹在中间，</span><span style="font-family: 微软雅黑;font-size: 14px;">这说明了因子的有效性。随之而来有趣的一个设想是，如果可以做风险对冲，多头第一分位股票，做空最差分位股票，可能基本能保证收益率永远为正。</span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;"><br />接下来我们延续之前个股的回测思路，将行业看作个股，统计行业因子值，按照如下图所示的调仓规则进行行业的因子回测：<br /><br /></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMvWbCzmfFAXDTWBsHDRxwQOKibtUM7TOagibhAdDyG8qia0ictzkvTvW9kQ/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><br /></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 14px;"><strong><span style="font-family: 微软雅黑;font-weight: bold;">净资产收益率</span></strong><strong><span style="font-family: 微软雅黑;">行业因子回测：</span></strong><span style="font-family: 微软雅黑;"><span style="font-family: 微软雅黑;">高</span>ROE行业(第一分位)不一定对应高回报<br /></span></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5065229722064662" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMLdAfB6oDu4p9Qw9xrhkAJF8LJLBq99husibfr9xMDT7fW6YiaRa1FaBQ/640?wx_fmt=png" data-type="png" data-w="1763" style="height: auto !important;" /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><br /></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 14px;"><strong><span style="font-family: 微软雅黑;font-weight: bold;">净资产收益率行业因子回测：</span></strong><span style="font-family: 微软雅黑;">各调仓期因子行业分位组变化</span></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1.0613636363636363" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMHLb7aGtoMTOAsXelcmZZXVibX3hiblDpMY72T3uDrKD7W27THhr0ibkXw/640?wx_fmt=png" data-type="png" data-w="880" style="height: auto !important;" /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><br /></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 14px;"><strong><span style="font-family: 微软雅黑;font-weight: bold;">市净率行业因子回测：</span></strong></span><span style="font-size: 14px;font-family: 微软雅黑;">行业内5分位组较3分位组筛选具备收益率优势，低平均市净率行业(5分位)回报率较大，市场回温后收益率反弹较快</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5182724252491694" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMUZibtcpGWzv5JYLMkhID7CPZDjpEaYdpDJP4tlqrkbhjTTGiaqqG9ibPg/640?wx_fmt=png" data-type="png" data-w="1806" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-align: left;margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 14px;"><strong><span style="font-family: 微软雅黑;font-weight: bold;">市盈率行业因子回测：</span></strong><span style="font-family: 微软雅黑;"><span style="font-family: 微软雅黑;">行业内</span>5<span style="font-family: 微软雅黑;">分位组较</span>3<span style="font-family: 微软雅黑;">分位组筛选具备收益率优势，低平均市盈率行业</span>(5<span style="font-family: 微软雅黑;">分位</span>)<span style="font-family: 微软雅黑;">回报率较大，市场回温后收益率反弹较快</span></span></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.507454128440367" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqM7qmG6LdddBoFr6SHA1yuPf6AKKRj2yKWuO12UmHG9IFvE5Sv6UlFjw/640?wx_fmt=png" data-type="png" data-w="1744" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-size: 14px;"><strong><span style="font-family: 微软雅黑;font-weight: bold;"></span></strong></span><br /><span style="font-size: 14px;"><strong><span style="font-family: 微软雅黑;font-weight: bold;"></span></strong></span></section><section style="text-align: left;margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 14px;"><strong><span style="font-family: 微软雅黑;font-weight: bold;">总营业收入行业因子回测：</span></strong><span style="font-family: 微软雅黑;"><span style="font-family: 微软雅黑;">行业内</span>5<span style="font-family: 微软雅黑;">分位组较</span>3<span style="font-family: 微软雅黑;">分位组筛选具备收益率优势，高总和营业收入行业</span>(1<span style="font-family: 微软雅黑;">分位</span>)<span style="font-family: 微软雅黑;">回报率较大，市场回温后收益率反弹较快</span></span></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5183719615602035" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMBFsBzUl7FbcdJLr2uDwLu4xZSuCmoicBRC2BxZPSuj3p4u5XE3PXZMw/640?wx_fmt=png" data-type="png" data-w="1769" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;"><br /></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">刚刚讲的是比较纯粹的股票资产投资方式，这里我们也可以把前边讲的股票因子投资模型运用到房地产投资中或者城市进入中。<br /><br /></span><span style="font-family: 微软雅黑;font-size: 14px;color: rgb(2, 30, 170);"><strong>如果我们将每个城市看作是一项资产标的或者一只个股，那如何解释城市间房价涨幅差异也就是收益率差异呢？</strong></span></section><section style="text-align: left;margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMyGmaiac3l4ibulM1ibfaxPpfBRtvsF9ZDZR8pPWDb8QaDiaI7IE9l7PMuQ/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 14px;font-family: 微软雅黑;"><br />一个比较著名的与房价相关的指标就是小学生在校生人口，这里我们把每个城市2011-2014 年小学生在校生增速，与2014-2017年城市房价涨幅做散点图。<br /><br />图中的每一个点相当于一个城市，我们发现两者之间相关系数高达0.45，具有一定的线性关系，也就是说，<strong>可能小学生人口增速可以作为解释房价增长的驱动因子，或者用来预测未来房价涨幅。<br /><br />多因子择城回测：<br />单年份跨期因子建模：</strong>将288城房价三年涨幅与城市宏观指标三年涨幅&amp;指标绝对值建模，筛选城市房价影响因子。<strong><br />因子有效性回测检验：</strong>根据各因子综合权重，对各调仓周期城市得分进行综合评分，并排序分组，计算下一年房价分组平均收益率，以检验因子选取的长期有效性。（若历年城市评分分组排序与房价涨幅排序一致说明因子具备有效性。）</span><br /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-align: left;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMItQZd1tkGUcAqG5TTTSxlOGfuo3wjByq03GW9dB2Q2QsVd0g2hnoicg/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /><br /><span style="color: rgb(0, 0, 0);font-family: 微软雅黑;font-size: 14px;"><strong><br /></strong>我们得到常住人口、小学生人口、三产占比、房地产投资等指标，是房价因子的驱动因素，我们可以将这些指标归为：<strong>人口聚集、资金聚集/信贷扩张、市场供应</strong>三大类<strong>。我们该如何解释这些因子对房价的影响呢？</strong><strong><br /><br /></strong></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMyubAtJleh5BxMJicYiaJ8D97Xe2y05ynjAKma5VwWawUyVQxKeia2w10w/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="color: rgb(0, 0, 0);font-family: 微软雅黑;font-size: 14px;"><strong><br /></strong></span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-family: 微软雅黑;font-size: 14px;">从经济学角度看，我们可以把这些有效因子归为两大类<strong>，</strong><span style="color: rgb(0, 0, 0);"><strong><span style="font-family: 微软雅黑;font-size: 14px;">需求的推升因子</span></strong></span>——推升需求包括人口、资金聚集、城市化等指标，这些指标的增长可以推动对住宅的需求；</span><span style="color: rgb(0, 0, 0);"><strong><span style="font-family: 微软雅黑;font-size: 14px;">供给的收缩因子</span></strong></span><span style="font-family: 微软雅黑;font-size: 14px;">——地产供应与房价成负相关。结合两大类因素，当需求推升供给收缩的时候，均衡的房价就会上涨。<br /><br />我们<span style="font-family: 微软雅黑;font-size: 14px;">用有效因子</span>对<span style="font-family: 微软雅黑;font-size: 14px;"><span style="font-family: 微软雅黑;font-size: 14px;"><span style="font-family: 微软雅黑;font-size: 14px;">2013-2018年</span></span></span>288城进行了城市筛选回测，将这些城市每三年的投资期中分为五个分位组，可以得到<span style="font-family: 微软雅黑;font-size: 14px;">最好分位年化收益10.8%，相对于市场收益（β收益）的7.2%，有3.6%的超额α收益</span>，而最差分位只有4.6%。1、2分位组城市基本持续跑赢市场收益率；3、4、5分位组城市基本持续跑输市场收益率，投资中应当对这些城市进行适当规避。<br /><br /></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.5625" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMyRJicnZtYbjuQvQJibw9Hv9IiaCG2UEg77Z1xvh4UibWybRGwuibyRfLg7w/640?wx_fmt=png" data-type="png" data-w="1920" style="height: auto !important;" /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-align: left;margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 24px;"><strong><span style="font-size: 24px;font-family: 微软雅黑;font-weight: bold;"><br />NO.</span></strong><strong><span style="font-size: 24px;font-family: 微软雅黑;font-weight: bold;">2</span></strong></span></section><section style="text-align: left;margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><span style="font-size: 18px;"><strong><span style="font-size: 18px;font-family: 微软雅黑;font-weight: bold;">疫情元胞机<br /></span></strong></span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.75em;"><br /></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">截至欧洲中部时间29日18时(北京时间30日零时)，全球新冠肺炎确诊病例达638146例，死亡病例达30105例，疫情已影响202个国家和地区。<br /></span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><br /></span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">下图是截至3月26日的全球疫情地图，按国家统计的已确诊感染新冠病毒的人数（后文简称为：确诊人数），可见比较严重的几个国家有伊朗，欧洲，美国等。</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.7692307692307693" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMy9449Cz8gYbv4pLYhqfTG7LZgBBJUiapAPaPcpz8Yj9mvibP7sR2EaHQ/640?wx_fmt=png" data-type="png" data-w="936" style="height: auto !important;" /><br /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">我们以意大利和美国为例，看目前的疫情现状。</span><strong><span style="font-family: 微软雅黑;font-size: 14px;"><br /><br />意大利：</span></strong><span style="font-family: 微软雅黑;font-size: 14px;">意大利西北部是意大利国内较为严重地区，以伦巴底地区为中心，后面将会以伦巴底地区的米兰市作为模拟的区域。</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;<br /></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1.3820459290187892" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMDB6NlXWib9EsnU5n5azAqJNNPqaE9FTIHgnfUP5C42icpzPM9ic2Bn0VQ/640?wx_fmt=png" data-type="png" data-w="479" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;"><br /></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">下图为意大利伦巴底地区近一个月的确诊人数变化，可见从3月开始增长速度是在增加中。</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.6987179487179487" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqM1JnJeVibiaWqYorumR9NcQ1HDnfvDMUlgunH4xaallf6S4mMRwt0qLxQ/640?wx_fmt=png" data-type="png" data-w="936" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><br /><strong>美国：</strong>下图是美国以州为单位的确诊人数，最严重的州是纽约州，比第二名加州高出一个数量级，后面也会以纽约州的纽约市作为第二个模拟区域。</span><br /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;<br /></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.561965811965812" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMm7Dfsvrx7aG4OibPt7vzv7bxtxhkAY654sgLU56SLROecMK8t8YJjxA/640?wx_fmt=png" data-type="png" data-w="936" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">下图为纽约州与伦巴底地区确诊人数的图表，可见纽约州虽然较伦巴底人数大幅上升的时间晚一些，但纽约州在近期的增长速度较伦巴底大了很多。</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;<br /></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.6047008547008547" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMomd2ib5uevF0y3IoNkOTvLpwHuO7ibKXxAUo2jlrGYw6gcY4NotMKJ6w/640?wx_fmt=png" data-type="png" data-w="936" style="height: auto !important;" /><span style="font-family: 微软雅黑;font-size: 14px;"><br />确诊人数的增长和许多因素相关，比如<strong>病毒检测速度</strong><strong>、病毒检测成功率、接受病毒检测的人数、出现症状的人数的增加</strong>等，而且对于目前所知的新冠病毒的一个特性，无症状感染者的存在也对确诊人数产生不小影响，<strong>本文中的模拟以感染者只有一定概率出现症状为前提。</strong></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="color: rgb(0, 0, 0);"><strong><span style="color: rgb(0, 0, 0);font-family: 微软雅黑;font-size: 14px;">本次以SIR流行病学传播模型为基础，对城市尺度的地理空间结合元胞自动机进行模拟。</span></strong></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-size: 14px;"><span dir="LTR" style="font-family: 微软雅黑;"><br /><strong>SIR模型：</strong></span><strong><span dir="LTR" style="font-family: 微软雅黑;">S代表易感人群（</span><span dir="LTR" style="font-family: 微软雅黑;color: rgb(34, 34, 34);font-weight: bold;background: rgb(255, 255, 255) none repeat scroll 0% 0%;">S</span><span dir="LTR" style="font-family: 微软雅黑;color: rgb(34, 34, 34);background: rgb(255, 255, 255) none repeat scroll 0% 0%;">usceptible</span><span dir="LTR" style="font-family: 微软雅黑;"><span style="font-family: 微软雅黑;">），</span>I代表被感染人群（</span><span dir="LTR" style="font-family: 微软雅黑;color: rgb(34, 34, 34);font-weight: bold;background: rgb(255, 255, 255) none repeat scroll 0% 0%;">I</span><span dir="LTR" style="font-family: 微软雅黑;color: rgb(34, 34, 34);background: rgb(255, 255, 255) none repeat scroll 0% 0%;">nfectious</span><span dir="LTR" style="font-family: 微软雅黑;"><span style="font-family: 微软雅黑;">），</span>R代表恢复健康或死亡人群（Recovered）<br /><br /></span></strong></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">传播模型以如下微分方程组表示：<strong><span style="font-family: 微软雅黑;font-size: 14px;">t为时间，β的倒数代表易感者与感染者接触时间，γ的倒数代表感染者恢复的时间，N为S,I,R三个人群的总数。<br /><br /></span></strong></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.3669250645994832" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMPBQvblCIzHEfYDjenZnK1EyPJICrS8lpicbGFnDg19fUFUwP0RTx0YQ/640?wx_fmt=png" data-type="png" data-w="1161" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">在这个模型中，不考虑自然增长的人数（出生与其他自然死亡）。<br /></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">让我们先看一个最简易模拟，下图为一个100x100的网格，每个格子代表一个人，初始状态蓝色为易感者（S），红色为随机出现的感染者（I），每个感染者可以一定概率感染其相邻的8个邻居，经过数个离散的传染步长，所有格子被感染。</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.75" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqM0SUGzVP4HUXZxG08AVd6kiaqLsMCialsRxzXRUoVicUibibyicxkHlNFXf1Q/640?wx_fmt=gif" data-type="gif" data-w="400" style="height: auto !important;" /><span style="display: none;line-height: 0px;">‍</span><span style="display: none;line-height: 0px;">‍</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">再看一个模拟结果，下图中曲线，蓝色为S，绿色为I，红色为R。代表这次的流行病传播经过一次大增长后，最终达到绝大部分人恢复的状态。</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.75" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMBic5NXGGpibW6ZvPJwElXsB9atWMusPC1ZicySeQoVX0QPD1ARIIPNLEw/640?wx_fmt=png" data-type="png" data-w="644" style="height: auto !important;" /><span style="font-family: 微软雅黑;font-size: 14px;">下面我们对稍微真实一点的世界做个模拟，用SIR模型，<strong>针对新冠病毒我们稍微调整下模型为SCIR，其中C为携带者（Carrier）即无症状感染者，而由于对于R的数据我们目前仍比较难得到，模拟中我们只模拟到I，I人群被感染后都保持此状态。</strong><br /></span><br /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">先做一个米兰市的。由于我们研究的病毒传播大多数主要基于人与人之间的传播，哪里有人哪里就可能有感染的出现，所以我们先看看米兰市的人口分布。</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;<br /></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.8623962040332147" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqM2UjprXicEVUlcJfcG2Nl0OAlXkTdjNDbB2Waibogx2XOQUaNDGI8j2SA/640?wx_fmt=png" data-type="png" data-w="843" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;text-align: right;"><span style="font-family: 微软雅黑;font-size: 12px;color: rgb(136, 136, 136);">备注：按光谱波长由小到大顺序：蓝青绿黄橙赤</span><br /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><br />上图中，米兰的人口以方格方式做统计，每个方格为1公里x1公里，按每个方格人口数量计数，人口数量由小到大，对应方格颜色由蓝到红，<strong>红色为人口密度最大的地方，也可见城市中心在红色区域及周围。</strong></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">下面就以SCIR模型和元胞（方格）进行模拟。<br /><br />首先我们假设，每个方格中的人会有一定概率流动到城市中其他方格中，代表人类的每日活动，人口流动我们使用地理距离衰减与交通通达数据结合的流动概率矩阵。每个方格中也具有一定的感染参数即β与γ（γ本次模拟暂时不考虑），在某个方格中活动的人会因这个方格的β有一定概率被感染。<br /><br />感染者出现症状的概率目前也是难以知道，在模拟中假设为0.1。时间以天为计数，即每一个计算步长代表一天，计算一天内传播结果，我们将模拟60个步长（60天）。</span></section><section style="margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span dir="LTR" style="font-family: 微软雅黑;font-size: 14px;"><span style="font-family: 微软雅黑;">模拟过程设为</span>4种情况，分别模拟传播全过程：</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-size: 14px;font-family: 微软雅黑;">a.&nbsp;<span style="font-family: 微软雅黑;">人口正常流动，个人无防护</span></span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-size: 14px;font-family: 微软雅黑;">b.&nbsp;<span style="font-family: 微软雅黑;">人口正常流动，个人做好防护</span></span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-size: 14px;font-family: 微软雅黑;">c.&nbsp;<span style="font-family: 微软雅黑;">人口限制流动，个人无防护</span></span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-size: 14px;font-family: 微软雅黑;">d.&nbsp;<span style="font-family: 微软雅黑;">人口限制流动，个人做好防护</span></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">个人做防护会以β参数的变化来体现。<br /><br /></span><strong><span style="font-family: 微软雅黑;font-size: 14px;background-color: rgb(2, 30, 170);color: rgb(255, 255, 255);">a. 人口正常流动，个人无防护</span></strong></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">下图中每个方格的颜色代表方格中感染人数与总人数之比，比值由小到大，为由蓝到红。</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.7" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqMg7989wYJwIDpfnu22hVeyxRbpQev3EfB5bxPcHTX3jB2ibzHkpXAPQg/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">下图为变化曲线，绿色为S（易感者数量），红色为C（感染者数量，包括无症状感染），蓝色为I（有症状感染者）。<br /><br /><strong>可见在30天后增长速度开始减小，直到60天几乎所有人被感染。</strong></span><br /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMcicNdcEElWjjqTpuSe9qNoAlovj3riaJyURMnRtNTFvF8x4Hg6nkrp9A/640?wx_fmt=png" data-type="png" data-w="834" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><strong><span style="font-family: 微软雅黑;font-size: 14px;background-color: rgb(2, 30, 170);color: rgb(255, 255, 255);">b. 人口正常流动， 个人做好防护</span></strong><br /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.7" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqMibYf5jLKVicBcNuCiaXqQ12O73Xzib463QFwmd5DPkGA3h2d9icIWYUFfNA/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqM8F6WAkvVroN4CcorFhK8P6EpbyyUMNy4Pcyrrd4oUTsWL39SibTDM6g/640?wx_fmt=png" data-type="png" data-w="693" style="height: auto !important;" /><span style="font-family: 微软雅黑;font-size: 14px;">为了稍微更加接近真实一点，将传播按时间分为三段：<br />第一段让人口都自由流动，个人无保护;<br />第二段以abcd情况来设置人口是否加以限制，个人保护做很好;<br />第三阶段（可看作恢复期）人口流动减少限制，个人保护有所放松不够完全。<br /><br /><strong>可以看到感染人数增长变少很多，而第三阶段个人保护变差数量便会猛增。</strong></span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><strong><span style="font-family: 微软雅黑;font-size: 14px;background-color: rgb(2, 30, 170);color: rgb(255, 255, 255);">c. 人口限制流动， 个人无防护</span></strong></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.7" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqMrVOwWvYpUdu0TvIVuqVRSknFWmNVk8IVlh8IGKVWEvhk3baYmGe2iaQ/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMhdEn64Dds1uCYlYGc3oEDsu6Ny7VVp4rQt3RP7B1AlKDmpF4gZbCVQ/640?wx_fmt=png" data-type="png" data-w="588" style="height: auto !important;" /><span style="font-family: 微软雅黑;font-size: 14px;">可以看到，<strong>个人没有保护的情况下，在第二阶段虽然限制了人流，但仍有很大的增速，虽然增长没有a情况恐怖，但也达到了1/3的总人口数量被感染。</strong>（此情况，限制了方格间人口流动，但没有限制方格内的社区间互动）。</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="margin-left: 8px;margin-right: 8px;"><strong><span style="font-family: 微软雅黑;font-size: 14px;background-color: rgb(2, 30, 170);color: rgb(255, 255, 255);">d. 人口限制流动， 个人做好防护</span></strong></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.7" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqM8nKks77UvQJzCb6iadCBdmoy3vatEWXtt2wsxyy9EibLx4vKtQhUnfcg/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /></section><section style="margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMc7EBptFPsic99JRWiaKtuA4ggubibD6ydqvbpkJTQzccibArj17v30jfHA/640?wx_fmt=png" data-type="png" data-w="637" style="height: auto !important;" /><span style="font-family: 微软雅黑;font-size: 14px;">d情况的结果与b类似，可以看到个人防护对于减弱传播更加显著。</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">同样的方式我们看看对纽约市的模拟，纽约市总人口为780万，平均人口密度高于米兰市很多。</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">下图是全美国的增长对比，可见纽约市一骑绝尘。</span></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.7478632478632479" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMESwLia7ztib8ofRrWiaph3HruzLIiaKEib74aBeXg6QNcRUnPgXeSOleCsQ/640?wx_fmt=png" data-type="png" data-w="936" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.6602564102564102" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMbfTBeXvZZhGeSeCauY7Gzf35MaicIYHhQD59a8yLBIzZMHWwxAnJM7Q/640?wx_fmt=png" data-type="png" data-w="936" style="height: auto !important;" /><span style="font-family: 微软雅黑;font-size: 14px;"><br />纽约市人口分布</span></section><section style="text-indent: 0px;text-align: center;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"> <br /></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.7510729613733905" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMgcFFUh6XYB62xIwaR8qvAggVmIuibwfzCaoo85l5tRrPbIEqicce0m6A/640?wx_fmt=png" data-type="png" data-w="699" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;"><br />纽约市a情况，人口正常流动，个人无防护</span><br /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.6" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqM1GdGFraV1PrLfWauMxxyrCLtWoGhFTwibPsDNhcibAicSo1q5d4T73Yiaw/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMRYMxZibjvuvEsgBrqGker3V48CQXJTFwgnVtaia4HdPbqUwRhXhBbgkQ/640?wx_fmt=png" data-type="png" data-w="631" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">纽约市b情况，人口正常流动， 个人做好防护</span></section><section style="margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.6" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqM9jkBvn30wmiaQNA2rwFkwj9FG0r8jZicZgvTDwSCS3EOHGH4IWvlI3iaA/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /><span style="display: none;line-height: 0px;">‍</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMwibuvnNpvWEw8YeRt4UfFF47RoxBnmExwfviaQhs2KbR34EOOBM02G5g/640?wx_fmt=png" data-type="png" data-w="583" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;纽约市c情况，人口限制流动， 个人无防护</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.6" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqMKTp5nzbpX6yugr0Anp095tzUPnz4Vias3W5K4FvqFN7fJvrR3krfwrg/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /><span style="display: none;line-height: 0px;">‍</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqM4sdjgjDobVr4e47zrDF1ZUQq4Uqm8zD6b0X0Mh7GJ3rbRE13bD5FVg/640?wx_fmt=png" data-type="png" data-w="613" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">&nbsp;纽约市 d情况，人口限制流动， 个人做好防护</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img data-ratio="0.6" data-src="https://mmbiz.qpic.cn/mmbiz_gif/AJkYaTAujIxs2NwP396r8nE13icJz5EqMW4pwpqWgCMse4WWYtdexDhKiaiap0jRkBRWVgewNnxhLic6sSFEdb4nCg/640?wx_fmt=gif" data-type="gif" data-w="1000" style="height: auto !important;" /><span style="display: none;line-height: 0px;">‍</span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="1" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqM5FIhPx5Ip61A46mpbBrmOuZZ7ib4QJyK1VhmfD9mc5KhQBeHX92M1zQ/640?wx_fmt=png" data-type="png" data-w="729" style="height: auto !important;" /></section><section style="text-indent: 0px;margin-left: 8px;margin-right: 8px;"><span style="font-family: 微软雅黑;font-size: 14px;">纽约市与米兰市的模拟结果，在增长曲线上形状相似，由于人口密度和地理交通等的不同，感染人数的比例不尽相似。因为这个模拟是基于较为简单的数据与模型，很多人类社会复杂行为与情况都未能考虑进去，因此模拟结果与现实仍有差距。<br /><br />从模拟中，</span><span style="color: rgb(2, 30, 170);"><strong><span style="font-family: 微软雅黑;font-size: 14px;">我们也可以看到，个人防护对传播的影响权重还是比较大的，因此在我们现在疫</span></strong><strong><span style="font-family: 微软雅黑;font-size: 14px;">情仍未完全结束阶段，做好个人保护还是最有效保护自己也是保护周围其他人的好方式。</span></strong></span></section><section style="margin-left: 8px;margin-right: 8px;line-height: 1.5em;text-align: center;"><span style="font-size: 14px;color: rgb(0, 0, 0);"><strong><span style="font-size: 14px;font-family: 微软雅黑;letter-spacing: 1px;font-weight: bold;background: rgb(255, 255, 255) none repeat scroll 0% 0%;"><br />↓↓↓ 戳原文链接，可观看本次直播录屏 ↓↓↓<br />还有更多禾略地产行业科普课程等你来解锁~<br /><br /></span></strong></span></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.768409818569904" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIxs2NwP396r8nE13icJz5EqMgEmt4KTezHzNeVhBWA8Pc6KU7vw8hzD45ib918XCUZLxQ8hj8kceMuA/640?wx_fmt=png" data-type="png" data-w="937" width="493" height="378" style="height: auto !important;" /></section><section style="text-align: center;margin-left: 8px;margin-right: 8px;"><br /></section><section style="font-variant-numeric: normal;font-variant-east-asian: normal;white-space: normal;text-align: center;line-height: 1.75em;letter-spacing: 0.54px;min-height: 1em;max-width: 100%;box-sizing: border-box;overflow-wrap: break-word;margin-left: 8px;margin-right: 8px;"><span style="box-sizing: border-box;color: rgb(178, 178, 178);font-size: 14px;max-width: 100%;overflow-wrap: break-word;">——&nbsp; END&nbsp; ——<br style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;" /></span><br /></section><section style="font-variant-numeric: normal;font-variant-east-asian: normal;white-space: normal;text-align: center;line-height: 1.75em;letter-spacing: 0.54px;min-height: 1em;max-width: 100%;box-sizing: border-box;overflow-wrap: break-word;margin-left: 8px;margin-right: 8px;"><span style="box-sizing: border-box;font-size: 12px;max-width: 100%;overflow-wrap: break-word;">猜你想再看<br style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;" /></span></section><section style="font-variant-numeric: normal;font-variant-east-asian: normal;text-indent: 0em;white-space: normal;text-align: center;line-height: 1.75em;letter-spacing: 0.54px;max-width: 100%;box-sizing: border-box;overflow-wrap: break-word;background-color: rgb(255, 255, 255);margin-left: 8px;margin-right: 8px;"><br /></section><section style="font-variant-numeric: normal;font-variant-east-asian: normal;text-indent: 0em;white-space: normal;text-align: left;line-height: 1.75em;letter-spacing: 0.54px;max-width: 100%;box-sizing: border-box;overflow-wrap: break-word;background-color: rgb(255, 255, 255);margin-left: 8px;margin-right: 8px;"><span style="font-size: 12px;"><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"><span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">城市：</span></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">|&nbsp;</span></span><span style="box-sizing: border-box;font-size: 12px;max-width: 100%;overflow-wrap: break-word;"><a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831649&amp;idx=1&amp;sn=191239418c15b0c6f395c843415da5fd&amp;chksm=8351793eb426f028970ac64031955167bfde997cdc96375bfb3bce25b5076f1458e11be2be27&amp;token=217203186&amp;lang=zh_CN&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">徐州</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831649&amp;idx=4&amp;sn=3a8acfb05820bbd38cd7b15a58e92ec9&amp;chksm=8351793eb426f028dfd96ec6ffc5239a84aaf25b6643813aa6b4a597b9a3215e7ab25e2b4eaf&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">宿迁</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831649&amp;idx=3&amp;sn=1fcdc66fac79d5ba9504bc24314a14f9&amp;chksm=8351793eb426f02829eef9ba1dfcb8c3e91edb05d3c1d34c548b82f618928834f1da5907d2e7&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">淮北</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831649&amp;idx=2&amp;sn=18d65f24543e71ff6bc70eb1cb0a7bde&amp;chksm=8351793eb426f028b98805f0f7555bfc57e3aefe6c76e7ca8df0369ad5dcc4a593a011a9b029&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">唐山</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831649&amp;idx=5&amp;sn=9f550e5d1f6bd3becc92df723adedd61&amp;chksm=8351793eb426f0289523b13ecd4fcb3d227a3cb259a09e504d388ace5a5eb25ece3aecfe8d46&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">天津</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831491&amp;idx=4&amp;sn=4c4fb5ce9d25c1fe6012d719c5878c82&amp;chksm=8351799cb426f08a8a6b9f35c8db84ceac56401b6da4a6429d1bc5e3339251db372a5045c242&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">深汕</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831603&amp;idx=5&amp;sn=c2d8bae147d4a2d86ec992c50c39ddad&amp;chksm=8351796cb426f07a50b1acbe92593aabba12c3fb95e9966d93ecad99918dbcf654b9ce767405&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">哈尔滨</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831491&amp;idx=3&amp;sn=1e787f725d62f227dbc6c33d0b9ea3eb&amp;chksm=8351799cb426f08accd8896c160b37e7a4436d21e1fbf2cc596763115db5ef6e04dc914ce478&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">兰州</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831603&amp;idx=4&amp;sn=048088acd651254d77cc238d71b1af04&amp;chksm=8351796cb426f07a7c36e33460f244db68a856502151c73820b314470b7e24412b9a8b6dcd5b&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">常德</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831491&amp;idx=2&amp;sn=b6295a149a38a026e886d81014b568f3&amp;chksm=8351799cb426f08a8a8d7adbd8721956fd91c59be8bd1ec35d4f9963a11e7e67bee72cd49405&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">南宁</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831603&amp;idx=8&amp;sn=0efaff09c26e604d7aa5c29376c129ad&amp;chksm=8351796cb426f07abb37dd11a0cfe941868be2b543feebf288460418759254327292658947ae&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">桂林</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831603&amp;idx=3&amp;sn=12f08ffb076544edcbc24e91bc3d87d7&amp;chksm=8351796cb426f07a1cd4530a9033d462d4732c500dcdda723bdc3a87f4d55f1c62f657a4cb77&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">柳州</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831603&amp;idx=6&amp;sn=0a89c4ab17039cec25754aa111b87308&amp;chksm=8351796cb426f07a6fdc14a1c0e877928f2fa46798a8b592b2b2023ad1c65081bbc80b2fafad&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">蚌埠</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831603&amp;idx=7&amp;sn=1bc72e377ffc3b621c2886d68c437515&amp;chksm=8351796cb426f07adc8c50a3e1409197892c508ad9c27a6b52f8e4dde12740baf5674f5a7fa6&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">合肥</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831491&amp;idx=1&amp;sn=10e3d481f7fd0ff46dafe2648cd3ddfb&amp;chksm=8351799cb426f08a5118705d6b85487fa97dd013a2aee842be719ee13086aab8dee370b54185&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">南京</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831603&amp;idx=1&amp;sn=9ffda0c7d9667d6700966a8bab12eccf&amp;chksm=8351796cb426f07a4e94a2471b2d59264ed4460e0567c63095fad9c5704541a546d7bc23584a&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">上海临港</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831065&amp;idx=1&amp;sn=2ffb60d98d02ebcab655c55d34d0acbf&amp;chksm=83517746b426fe509cc721e0e3acf05fd1f60b8695dc3b66c08c0a7aa917e7471b013b02c2c2&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">太原</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830804&amp;idx=1&amp;sn=f571d8218b897b21571a6b2f497d3a1b&amp;chksm=8351744bb426fd5d509591673f4082563a02342283f53dfda255ad33304e6746d6448051b9ea&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">温州</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830454&amp;idx=1&amp;sn=4e7c3289190e2a69c5fb20f2ae8a6d94&amp;chksm=835175e9b426fcffa5f65cafe5274b1c296caf1a51e13ef4c7920c5a18847bef3c7b13c2bfd0&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">昆明</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830295&amp;idx=1&amp;sn=f680ffa2ddf52783e9a7730971520d48&amp;chksm=83517248b426fb5e0efc1e5c62d15b173e4d23ab7aafaab82c6ce861e98d96271fe5dc7db798&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">嘉兴</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830278&amp;idx=1&amp;sn=8441ac780477cd9def8d4e9d7866f143&amp;chksm=83517259b426fb4f93ff50f1c07d7b830f16ec4d1e0c23f64ef15a78a056ae301274ffbb8ec3&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">重庆</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830196&amp;idx=1&amp;sn=7a599cf338734c1d41c6fa16005b1641&amp;chksm=835172ebb426fbfdda6873adbeddc124ae670de675a7c36d11977106150a1d924572ea70f299&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">成都</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830221&amp;idx=1&amp;sn=f5994dbfe9fa00ffce4b5be1a69f3244&amp;chksm=83517292b426fb8419e771cf48ea94de01fc7dc909b4e8c2759c6423b8be6080bc5bd1c248cc&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">深圳</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649829995&amp;idx=1&amp;sn=cd78421e4f2e724f552f8eefc65e0236&amp;chksm=835173b4b426faa26aed46ed566bc1f8ffa11498370fed14fa9d0690795a3eff5a186c63a03d&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">上海</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649829512&amp;idx=1&amp;sn=421f2b766d75009082de8fc1e81cd8d2&amp;chksm=83517157b426f84197c93fd852a3e3f93019c9d81e099784ad0aa09f326ca9dd33a0edb7cfd7&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">珠三角</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649829480&amp;idx=1&amp;sn=c77baf137c109f1017170a708548d37b&amp;chksm=835171b7b426f8a1d942708988b8f4bd875366f5928d1db99470ccad6958aa0c8cd47b292c23&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">雄安新区</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=401964235&amp;idx=1&amp;sn=8839375241e6a7e69f49aec108ca1ad6&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">无锡</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=203026648&amp;idx=1&amp;sn=466dca69ff3eb746e2e5c21831d57f0f&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">北京</a>&nbsp;|&nbsp;<br style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;" /></span></section><section style="font-variant-numeric: normal;font-variant-east-asian: normal;text-indent: 0em;white-space: normal;text-align: left;line-height: 1.75em;letter-spacing: 0.54px;max-width: 100%;box-sizing: border-box;overflow-wrap: break-word;background-color: rgb(255, 255, 255);margin-left: 8px;margin-right: 8px;"><span style="font-size: 12px;"><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"><span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">热点：</span></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"></strong><span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">|&nbsp;</span></span><span style="box-sizing: border-box;font-size: 12px;max-width: 100%;overflow-wrap: break-word;"><a href="http://mp.weixin.qq.com/s?__biz=MzIxMTUxMzE2Mw==&amp;mid=2247485505&amp;idx=1&amp;sn=90a4482d0ec14f8a4d441f77c653806c&amp;chksm=97557265a022fb7385559a6648c54242c721582b3811ad664360ea1e6f562f0f62264852c20c&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" data-itemshowtype="0" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">深圳土拍</a></span><span style="font-size: 12px;"><strong style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;"><span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">&nbsp;</span></strong><span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">|&nbsp;</span></span><span style="box-sizing: border-box;font-size: 12px;max-width: 100%;overflow-wrap: break-word;"><a 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href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830578&amp;idx=1&amp;sn=73f5149b299d5ce19a433c365eedee83&amp;chksm=8351756db426fc7b173558a1765830766ec5f7fb387e652250f10a106ef6490821f809722cfb&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">中美贸易战</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830503&amp;idx=1&amp;sn=2fae9eec64a6ed71f0c4ee9e4e9bafe7&amp;chksm=835175b8b426fcaec41bb2a484ef939ac78474c77acde2d96a6f7f8b61a0f4ade630c13e7f90&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">粤港澳</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830398&amp;idx=1&amp;sn=ffd40b9cb7730bd712d8f053280d6fa9&amp;chksm=83517221b426fb37e97b45db61547227724f5a09e6a2a0484a55475066ac41fc1b0165954d0d&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">万科商业</a>&nbsp;|&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830360&amp;idx=1&amp;sn=3cea24af7ebf848fde74c52538f111e5&amp;chksm=83517207b426fb11a1ae1c301117e9626ba09012aa9d8b4d8f722e45423ecb7e63987f50bec5&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">2018年走势</a>&nbsp;|<br style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;" /></span></section><section style="font-variant-numeric: 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100%;overflow-wrap: break-word;"></strong><span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">|&nbsp;</span></span><span style="box-sizing: border-box;font-size: 12px;max-width: 100%;overflow-wrap: break-word;"><a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649831987&amp;idx=1&amp;sn=8553537eb64de48a9b7eb16564fe8988&amp;chksm=83517becb426f2fa0c63ef59ace65085334609b45795331170f0edb7f455d154c06d53aa85f7&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;overflow-wrap: break-word;">穿越熊市</a></span><span style="font-size: 12px;">&nbsp;<span style="box-sizing: border-box;max-width: 100%;overflow-wrap: break-word;">|&nbsp;</span></span><span style="box-sizing: border-box;font-size: 12px;max-width: 100%;overflow-wrap: break-word;"><a 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href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830698&amp;idx=1&amp;sn=27ffa7f097500e9e7fb23f99fdce51ef&amp;chksm=835174f5b426fde3854d2eec6dc6fd1c0c182faa0218d1b0ce833e50c860c23b062b88f914e0&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">高周转</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830656&amp;idx=1&amp;sn=dc61474f9d09133fcce2934476ea10c1&amp;chksm=835174dfb426fdc9575a9a316aef5c25d051f574d0cd96ae3d1cda189bca7c7b0b7447e403e4&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">房价预测</a>&nbsp;|&nbsp;<a href="http://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830457&amp;idx=1&amp;sn=37a5c454028fb849c2c5fce3b3575756&amp;chksm=835175e6b426fcf07c9d8fdee249e33edf0ae7f5684be2290c3145624ad430d880a10a654ebd&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">2018房地产报告</a>&nbsp;|&nbsp;&nbsp;<a href="https://mp.weixin.qq.com/s?__biz=MzAxMDEzOTgyNA==&amp;mid=2649830201&amp;idx=1&amp;sn=1816623486b879233513443f1df6ec59&amp;chksm=835172e6b426fbf07aa0f023c3ff79ca1cf11606fc2f2b66cfe773222e3fa1df7f92affa90b6&amp;scene=21#wechat_redirect" target="_blank" data-linktype="2" style="box-sizing: border-box;cursor: pointer;max-width: 100%;outline: 0px none currentcolor;overflow-wrap: break-word;">远郊定位&nbsp;</a>|&nbsp;<a 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