Global dynamics and sliding motion in A(H7N9) epidemic models with limited resources and Filippov control

Abstract

This paper investigates the effects of different control measures on the dynamics of A(H7N9) virus transmission from poultry to human. An SI-SIR model with nonlinear incidence and recovery rates is formulated to evaluate the combined impacts of government intervention strategies and available hospital resources. The global stability of the disease-free and endemic equilibria is obtained by constructing Lyapunov and Dulac functions. Furthermore, based on the threshold policy, the SI-SIR model is extended to a novel three-dimensional Filippov one to represent the control measures being triggered once the total number of infected poultry and human reaches the tolerant level Ic. Model solutions are able to approach either one real equilibrium or the pseudo-equilibrium, depending on the tolerant threshold. Our results suggest that in order to diminish the outbreak of A(H7N9) virus or lead the number of infections to an expected level, it requires not only adequate hospital resources and certain government interventions, but also a good threshold policy.