Global Stability Analysis and Optimal Control for a Dynamical Model with Asymptomatic Infectious State

Abstract

In this paper, we present a dynamical model with asymptomatic infections and optimal control strategies based on a regular network. The basic model without control and basic mathematical results are obtained. Firstly, we obtain the basic reproduction number by using the method of the next generation matrix. Secondly, by taking advantage of the Lyapunov function, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R₀ < 1. By using generalized Bendixson-Dulac thereom, we prove that the unique endemic equilibrium is globally asymptotically stable when R₀ > 1. In addition, by using Pon-tryagin’s maximum principle, several reasonable optimal control strategies are suggested to the prevention and control the disease. Finally, numerical simulations are presented to verify the above theoretical results, and we perform sensitivity analysis by partial rank correlation coefficient(PRCC) methods. It is worth noting that asymptomatic infections have a greater contribution to the epidemic of diseases.