Global Stability Analysis of Two-Strain SEIR Epidemic Model with Quarantine Strategy

Abstract

AbstractIn this chapter, we study a two-strain SEIR epidemic model with bilinear and non-monotonic incidence functions in which the quarantine strategy is taken into consideration, this strategy is presented mathematically by u 1 and u 2, the first represents the efficiency of the quarantine strategy concerning the first-strain infection rate, and the second represents the efficiency of the quarantine strategy concerning the second-strain infection rate. By using the new generation matrix method, we have shown that the model has four equilibrium points and two basic reproduction numbers \(R_0^1\) and \(R_0^2\) that depend on u 1 and u 2. Using the Lyapunov’s method we have shown the global stability of different equilibrium points, this stability depends on \(R_0^1\) and \(R_0^2\). Finally, we have given two types of numerical simulations, the first to confirm the theoretical and to illustrate the effectiveness of quarantine to minimize the infection in the population.KeywordsTwo-strainEpidemic modelBilinear incidenceNon-monotone incidenceQuarantine