THE DYNAMICS AND THERAPEUTIC STRATEGIES OF A SEIS EPIDEMIC MODEL

Abstract

Based on an epidemic model which Manvendra and Vinay [Mathematical model to simulate infections disease, VSRD-TNTJ3(2) (2012) 60–68] have proposed, we consider the dynamics and therapeutic strategy of a SEIS epidemic model with latent patients and active patients. First, the basic reproduction number is established by applying the method of the next generation matrix. By means of appropriate Lyapunov functions, it is proven that while the basic reproduction number 0 < R0 < 1, the disease-free equilibrium is globally asymptotically stable and the disease eliminates; and if the basic reproduction number R0 > 1, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic. Numerical investigations of their basin of attraction indicate that the locally stable equilibria are global attractors. Second, we consider the impact of treatment on epidemic disease and analytically determine the most effective therapeutic strategy. We conclude that the most effective therapeutic strategy consists of treating both the exposed and the infectious, while treating only the exposed is the least effective therapeutic strategy. Finally, numerical simulations are given to illustrate the effectiveness of the proposed results.