The control of an infectious disease in a two stages SIRS model with a dualvaccination program

摘要

The main objective of this paper is to control an infectious diseaseby carrying out a vaccination program in a SIRS model where primaryand secondary infected (or susceptible) individuals are different in infectivity(or susceptibility) and recovery rate. Vaccination program tobe performed by vaccinating two different percentages of primary andsecondary susceptible individuals. To understand the behavior of infectionwe compute the basic reproduction number R0, and discuss it’srelationship with the existence, stability and bifurcation of equilibriums.Also we obtain a threshold for vaccine coverage percentage in order theinfection to be controlled.