INVESTIGATING THE EFFECTS OF TREATMENT, USE OF STERILE INSECT TECHNIQUE AND ASYMPTOMATIC OCCURRENCE ON A ZIKA VIRUS DISEASE MODEL

OPTIMAL CONTROL ANALYSIS OF ZIKA VIRUS DISEASE MODEL

Abstract

Zika virus disease is a flavivirus disease caused by the zika virus and transmitted amongst humans through the bites of an infectious female Aedes aegypti mosquitoes. It can also be transmitted through sex, blood transfusion and during pregnancy. In this work, a system of nonlinear ordinary differential equations was used to present a new model for the disease. The model incorporates treatment and vector control using sterile-insect technology (SIT). The model also incorporated asymptomatic cases to show how it affects the disease dynamics. The model was shown to be well-posed epidemiologically. The existence of unique solutions to the system was also established. Sensitivity analysis using the normalized forward sensitivity approach was carried out to show the key parameters affecting the dynamics of the disease. Numerical simulation showed that the occurrence of asymptomatic cases, human contact rate with mosquitoes and probabilities of transmission increase the endemicity of the disease. Optimal control analysis was done using Pontryagin maximum principle to show the number of infected humans that will be treated and proportion of SIT mosquitoes that will be introduced for optimal control of the disease. Plots were used to illustrate the effects of the controls. The results of the analysis showed that combining both controls produced better results than when each control was deployed independently of each other. In conclusion, we recommend that intervention measures for diseases caused by vectors should incorporate controls that can reduce the spread of the disease in both the human and vector population.