Bat-borne rabies is a viral infection caused by lyssaviruses. To explore the complex interaction between bats and cattle, we develop a periodic compartment system with seasonality, temperature-dependent incubation period and different control measures. We derive the basic reproduction number ${\mathcal{R}}_0$ and show it determines the global dynamics. In particular, we prove the non-existence of positive periodic solutions in the critical case where ${\mathcal{R}}_0=1$. Numerically, we observe that sufficient long time-varying incubation periods could potentially increase the disease outbreak risk.

中文翻译：

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具有周期性潜伏期的蝙蝠传播狂犬病模型的阈值动力学

蝙蝠传播的狂犬病是由狂犬病病毒引起的病毒感染。为了探索蝙蝠与牛之间的复杂相互作用，我们开发了一种具有季节性，温度依赖型潜伏期和不同控制措施的周期性间隔系统。我们得出基本的繁殖数${\mathcal{[R}}_0$并显示它决定了全局动力学。特别是，我们证明了在以下关键情况下不存在正周期解${\mathcal{[R}}_0=\mathrm{1个}$。在数值上，我们观察到足够长的随时间变化的潜伏期可能会增加疾病暴发的风险。