Analysis of Zika virus dynamics with sexual transmission route using multiple optimal controls

Abstract

In this paper, we formulate and analyse a nonlinear optimal control problem for a Zika virus (ZIKV) infection model with sexual transmission route. An existing deterministic 11-dimensional autonomous system of differential equations is extended to include five time-dependent control functions, namely personal protection, condom use, vaccination, treatment and spraying of insecticide. The necessary conditions for the existence of optimal control quintuple are shown, and we determine the control strategies to minimize the spread dynamics of the ZIKV in the population at the minimum cost of control implementation. The derived optimality system is solved numerically to demonstrate the effectiveness of the different combinations of the five optimal controls in curtailing the transmission and spread of the disease. More importantly, we conduct a cost-effectiveness analysis on the combinations of at least four optimal controls to ascertain the most cost-effective strategy that can be used to hamper the ZIKV spread in the population.

Keywords

• Optimal control
• Zika virus infection
• Pontryagin’S maximum principle
• Forward-Backward sweep method
• Cost effectiveness