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其中 <math>r_t</math> 代表感染者 (<math>r_t = 1</math>) 或者非感染者 (<math>r_t = 0</math>)。求解这个主方程，可以得到这样的解： <math>\tilde{P}_r(k) = \left(\frac r 2 \right)^k. </math><ref name="cotacallapa-hase">{{cite journal|last1=Cotacallapa|first1=M|last2=Hase|first2=M O|title=Epidemics in networks: a master equation approach|journal=Journal of Physics A|date=2016|volume=49|issue=6|page=065001|doi=10.1088/1751-8113/49/6/065001|bibcode=2016JPhA...49f5001C|arxiv=1604.01049}}</ref>

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~~==Interdependent networks==~~

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~~{{main|Interdependent networks}}~~

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An interdependent network is a system of coupled networks where nodes of one or more networks depend on nodes in other networks. Such dependencies are enhanced by the developments in modern technology. Dependencies may lead to cascading failures between the networks and a relatively small failure can lead to a catastrophic breakdown of the system. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. A recent study developed a framework to study the cascading failures in an interdependent networks system.<ref>{{Cite journal|author1=S. V. Buldyrev |author2=R. Parshani |author3=G. Paul |author4=H. E. Stanley |author5=S. Havlin |title = Catastrophic cascade of failures in interdependent networks|journal = Nature |volume = 464 |pages = 1025–28 |year = 2010 | doi=10.1038/nature08932 |issue=7291|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all |bibcode=2010Natur.464.1025B|arxiv = 0907.1182 |pmid=20393559}}</ref><ref>{{cite journal|first=Jianxi |last=Gao|first2= Sergey V.|last2= Buldyrev|first3= Shlomo |last3=Havlin|first4= H. Eugene|last4= Stanley|title=Robustness of a Network of Networks|journal=Phys. Rev. Lett.|year=2011|volume=107|pages=195701|url=http://havlin.biu.ac.il/Publications.php?keyword=Robustness+of+a+Tree-like+Network+of+Interdependent+Networks&year=*&match=all | doi = 10.1103/PhysRevLett.107.195701|bibcode=2011PhRvL.107s5701G|arxiv = 1010.5829|issue=19|pmid=22181627 }}</ref>

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