Authors: A Lahrouz, A Settati, H El Mahjour, M El Jarroudi et al. ↩

Abstract

In this work, we introduce the basic reproduction number for a general epidemic model with graded cure, relapse and nonlinear incidence rate in a non-constant population size. We established that the disease free-equilibrium state $E_{f}$ is globally asymptotically exponentially stable if $R_{0} < 1 $ and globally asymptotically stable if $R_0 = 1$. If $R_0 > 1 $, we proved that the system model has at least one endemic state $E_e$. Then, by means of an appropriate Lyapunov function, we showed that $E_e$ is unique and globally asymptotically stable under some acceptable biological conditions. On the other hand, we use two types of control to reduce the number of infectious individuals. The optimality system is formulated and solved numerically using a Gauss–Seidel-like implicit finite-difference method.

Reference

Physica A: Statistical Mechanics and its Applications 496 (2018): 299-317. DOI: 10.1016/j.physa.2018.01.007 ↩