Exact solution of generalized cooperative susceptible-infected-removed (SIR) dynamics.
Exact solution of generalized cooperative susceptible-infected-removed (SIR) dynamics.
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DOI：
10.1103/physreve.100.012307
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
Fatemeh Zarei;S. Moghimi-Araghi;Fakhteh Ghanbarnejad
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文献类型：
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作者：
Fatemeh Zarei;S. Moghimi-Araghi;Fakhteh Ghanbarnejad
在本文中，我们介绍了一个一般的框架，共同感染的合作可行性感染删除（SIR）的动态。我们首先解析求解了两个对称合作传染的SIR模型[L. Chen等人，欧罗巴Lett. 104，50001（2013）10.1209/0295-5075/104/50001]，然后在三个或更多个合作传染的对称场景中推广并精确求解模型。我们计算了转变点和序参量，即，受感染主机的总数。我们表明，系统的行为不会随着包含更多疾病而发生质的变化。我们还分析表明，有两个合作SIR动力学的鞍结分岔和过渡是混合的。此外，我们调查的对称解是稳定的初始波动。最后，我们探讨的参数集，引起不对称的情况下，即不对称的情况下，一个病原体的原发性和继发性感染率相对于另一个。此设置可导致更少的受感染主机、更高的流行阈值以及连续的转换。这些结果为更好地理解疾病生态学开辟了道路。
In this paper, we introduce a general framework for coinfection as cooperative susceptible-infected-removed (SIR) dynamics. We first solve the SIR model analytically for two symmetric cooperative contagions [L. Chen et al., Europhys. Lett. 104, 50001 (2013)10.1209/0295-5075/104/50001] and then generalize and solve the model exactly in the symmetric scenarios for three and more cooperative contagions. We calculate the transition points and order parameters, i.e., the total number of infected hosts. We show that the behavior of the system does not change qualitatively with the inclusion of more diseases. We also show analytically that there is a saddle-node-like bifurcation for two cooperative SIR dynamics and that the transition is hybrid. Moreover, we investigate where the symmetric solution is stable for initial fluctuations. We finally explore sets of parameters which give rise to asymmetric cases, namely, the asymmetric cases of primary and secondary infection rates of one pathogen with respect to another. This setting can lead to fewer infected hosts, a higher epidemic threshold, and also continuous transitions. These results open the road to a better understanding of disease ecology.