Modelling the dynamics of Zika in a population with two strains of the virus with optimal control and cost-effectiveness analysis

A new deterministic model incorporating two strains (African and Asian) of the Zika Virus, and which assesses the impact of heterogeneities caused by a previous infection from a different strain, different control measures connected to vectorial and human modes of transmission and superinfection, on the population dynamics of the disease, is formulated and rigorously analyzed. The model is shown to have a locally asymptotically stable disease-free equilibrium (DFE) when the associated effective reproduction number is less than unity. Sensitivity analysis is carried out to determine the parameters that are significant in driving the dynamics of the disease in the presence of the two strains, when the associated reproduction numbers and the population of humans and vectors are used as response functions. Our analysis and numerical simulations reveal that the key parameter that significantly affected the reproduction numbers of the model is the mosquito death rate (μV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _V$$\end{document}). The Pontryagin’s Maximum Principle is used to establish the necessary conditions for the existence of optimal control. Control parameters were introduced, strategies formulated and analysed with their attendant cost-effectiveness. The control strategy which combines effective condom use by individuals and vector control using insecticides significantly impacted the most in reducing the disease burden in the population with the best cost-effective result.