Dynamical analysis of a mathematical model of disease spreading on networks with symptomatic and asymptomatic infectors

Abstract

We establish an SEIaIdRS model to present the dynamics of epidemic on networks. Following the method of the next generation matrix, we derive the explicit formulas of the basic reproduction number R0. It shows that the asymptomatic infector plays an important role in disease spreading. By theoretical analysis, we find that the disease‐free equilibrium E0 is globally asymptotically stable if R0 ≤ 1; and the endemic equilibrium E+ is globally asymptotically stable if R0 > 1. At last, numerical simulations also show that the role that the asymptomatic infector plays in disease spreading on networks cannot be neglected.