Stability analysis and optimal control of avian influenza model on complex networks

Abstract

In this paper, an avian influenza model with saturation and psychological effect on heterogeneous complex networks is proposed. Firstly, the basic reproduction number ℛ0 is given through mathematical analysis, which is a threshold to determine whether or not the disease spreads. Secondly, the locally and globally asymptotical stability of the disease‐free equilibrium point and the endemic equilibrium point are investigated by using Lyapunov functions and Kirchhoff's matrix tree theorem. If ℛ0<1, the disease‐free equilibrium is globally asymptotically stable and the disease will die out. If ℛ0>1, the endemic equilibrium is globally asymptotically stable. Thirdly, an optimal control problem is established by taking slaughter rate and cure rate as control variables. Finally, numerical simulations are given to demonstrate the main results.

Sliding dynamics and optimal control of avian influenza model with saturated incidence rate

“…For the reason, the optimal control of the model is investigated by applying the dynamic programming method. Particularly, these results generalize and enhance the works presented in earlier studies [19, 20, 22].…”

“…Based on the idea of the threshold policy, the sliding dynamics of the model is studied by applying the Utkin equivalent control method. The theoretical results concerning sliding dynamics extend the work of earlier research [22,27]. • The prevailing research on optimal control has primarily revolved around the time period [0, T].…”

“…Researches concerning optimal control by using the Pontryagin maximum principle are one of the important research problems for avian influenza control theory, and there have been some results [19][20][21][22]. For example, Jung et al [19] formulated the optimal control by introducing elimination and quarantine measures to an susceptible-infective-susceptible-infected-recovered (SI-SIR) influenza model to reduce the number of infected individuals.…”

“…For example, Jung et al [19] formulated the optimal control by introducing elimination and quarantine measures to an susceptible‐infective‐susceptible‐infected‐recovered (SI‐SIR) influenza model to reduce the number of infected individuals. Ren et al [22] established an avian influenza model on complex networks and showed the existence of optimal strategy of slaughtering and treatment. However, these studies were focused on optimal control implemented over the entire infection period $$$ T $$$, which will take more time and economic cost.…”