We study the systems of partial differential equations with diffusion that model the dynamics of infectious diseases without life-time immunity, in particular the cases of cholera from Wang & Wang (2015, J. Biol. Dyn., 9, 233-261) and avian influenza from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829-2848). In both works, similarly to all others in the literature on various models of infectious diseases and more, it had to be assumed for a technical reason that the diffusivity coefficients of the susceptible, infected and recovered individuals, humans or birds, had to be identical in order to prove the existence of their unique solutions for all time. Considering that such uniform diffusivity strengths among the susceptible, infected and recovered hosts may not always be plausible in real world, we investigate the global well-posedness issue when such conditions are relaxed. In particular for the cholera model from Wang & Wang (2015, J. Biol. Dyn., 9, 233-261), we prove the global well-posedness with no condition on the diffusivity coefficients at all. For the avian influenza model from Vaidya et al. (2012, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829-2848), we prove the global well-posedness with no condition on the diffusivity coefficients if the spatial dimension is one, and under a partial condition that the diffusivity coefficients of the susceptible and the infected hosts are same otherwise.

中文翻译：

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没有终生免疫力的传染病模型的全球适宜性：霍乱和禽流感病例。

我们研究了具有扩散的偏微分方程系统，该系统对没有终生免疫力的传染病动力学进行建模，尤其是来自Wang＆Wang（2015，J.Biol.Dyn。，9，233-261）和Vaidya等人的禽流感。（2012，Discrete Contin.Dyn.Syst.Ser.B，17，2829-2848）。在这两种著作中，与文献中关于各种传染病模型的所有其他著作类似，并且更多，由于技术原因，必须假定易感，感染和康复的个体，人或鸟的扩散系数必须相同为了证明它们始终存在的独特解决方案。考虑到在易感，感染和恢复的宿主之间如此均匀的扩散强度在现实世界中可能并不总是合理的，当这种条件放松时，我们将研究全球适度性问题。尤其是对于Wang＆Wang（2015，J. Biol。Dyn。，9，233-261）的霍乱模型，我们证明了整体的适定性，而对扩散系数完全没有任何条件。对于Vaidya等人的禽流感模型。（2012，Discrete Contin。Dyn。Syst。Ser。B，17，2829-2848），我们证明了在空间维度为1的情况下，对于扩散系数没有任何条件的全局适定性，并且在部分条件下证明了扩散系数否则，易感宿主和被感染宿主的系数相同。对于Vaidya等人的禽流感模型。（2012，Discrete Contin。Dyn。Syst。Ser。B，17，2829-2848），我们证明了在空间维度为1的情况下，对于扩散系数没有任何条件的全局适定性，并且在部分条件下证明了扩散系数否则，易感宿主和被感染宿主的系数相同。对于Vaidya等人的禽流感模型。（2012，Discrete Contin。Dyn。Syst。Ser。B，17，2829-2848），我们证明了在空间维度为1的情况下，对于扩散系数没有任何条件的全局适定性，并且在部分条件下证明了扩散系数否则，易感宿主和被感染宿主的系数相同。