Global stability for a discrete SIR epidemic model with delay in the general incidence function - Aboudramane, Guiro; Ouedraogo, Dramane; Ouedraogo, Harouna (International Journal of Applied Mathematical Research, 2019)
In this paper, we construct a backward difference scheme for a class of general SIR epidemic model with general incidence function f. We use the step size h > 0, for the discretization. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, under the conditions that function f satisfies some assumptions. The global stabilities of equilibria are obtained. If the basic reproduction number R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>1, the endemic equilibrium is globally asymptotically stable.