Threshold dynamics of stochastic H7N9 model with Markov switching and hybrid strategy

This article aims to study the impact of different environmental states on the transmission dynamics of avian influenza A (H7N9) for poultry by using an epidemic model with general incidence rate and Markov switching. The model couples the essential roles of quarantine and hybrid strategy of vaccination and elimination. By establishing the basic reproduction number R0 as a sharp threshold for the spread of H7N9. When R0<1, the disease almost surely dies out exponentially. We use the compactness of space to prove that when R0>1, the disease almost surely persistent, and this method can be applied to other infectious disease models considering vaccination. In addition, under a mild extra condition, the ergodicity of the Markov process is proved. Our research indicates that: (i) theoretical results and sensitivity analysis show that implementing hybrid strategy is an effective method to control H7N9 propagation; (ii) under the influence of environmental switching, numerical simulations find that the transmission state of H7N9 will neutralize multiple regimes, leading to the possibility of multi wave transmission. This can be used to explain the multiple outbreaks of H7N9 in China.