MATHEMATICAL MODELING OF THE SPREAD OF VECTOR BORNE DISEASES WITH INFLUENCE OF VERTICAL TRANSMISSION AND PREVENTIVE STRATEGIES

Abstract

This work is aimed at formulating a mathematical model of the spread of vector-borne diseases with influence of vertical transmission and preventive strategies. Vector borne diseases are caused by viruses, bacteria, and parasites typically conveyed by mosquitoes. Certain illnesses transmitted by vectors include West Nile Virus, Malaria, Zika virus, Dengue fever, Rift valley fever, and Viral encephalitis induced by pathogens like bacteria, viruses, and parasites. The positive solutions of the model are presented and the theory of basic reproduction number  was used to study the model dynamical behaviour. When reduces; the diseases are wiped out of the population with time and vice versa. The disease free and endemic equilibria states of the model were determined and investigated to be locally and globally stable.We incorporated the use of Insecticide –Treated Nets (ITN), Indoor Residual Sprayings (IRS) and condom usage as preventive measures in the presence of treatment. Numerical simulations show that complete intervention measures, that is, the use of ITN, IRS and condom usage while placing the infected on treatment have valuable impact on the spread of vector-borne diseases.