On a new SIMVW epidemic model with vaccination and endemic testing

Abstract

A new epidemic model referred to as SIMVW is proposed which includes the following subpopulations: susceptible human, infectious human, susceptible vector, infectious vector and vaccinated human. The transmission vector is the anopheles mosquito for the malaria disease. The disease-free equilibrium points concerning the absence of infection in humans and/or mosquitoes are defined and discussed from a stability point of view. A set of simulated examples are performed mainly related to typical endemic situations which are tested for a malaria case study in the absence and in the presence of vaccination efforts. The vaccination efforts delete susceptible numbers which are transferred to the vaccinated subpopulation and include online feedback information on the susceptible subpopulation to adjust the control effort. The vaccination effects are mainly to improve the convergence rates to the equilibrium point, to decrease the numbers of susceptible individuals while increasing those of recovered ones and to reduce the basic reproduction number so that the range of stability of the disease-free equilibrium points is larger compared to the case of absence of vaccination.