Predicting the impact of education on malaria transmission with sensitivity analysis and optimal control

Abstract

Malaria is a catastrophic global disease transmitted to humans by bites from infected female Anopheles mosquitoes. Public awareness is a strong influencer on how individuals and groups of people perceive, respond to preventive interventions and other control measures. This work formulates mathematical model to study the impact of education on malaria control. In this work, the threshold parameter called control reproduction number was derived using next generation matrix method and used to study the global stability analysis of both the malaria-free equilibrium and malaria-endemic equilibrium. While the global stability of malaria-free equilibrium was assessed using comparison theorem, the global stability of malaria endemic equilibrium was done using non-linear Lyapunov function of Goh-Volterra type. Forward sensitivity analysis was carried out using the control reproduction number to identify the role of some critical parameters in malaria control. In the optimal control section, Pontryagin’s minimum principle was used to establish that, campaign to improve public usage of treated nets shows to be a very important optimal control parameter. The results of the sensitivity analysis and numerical simulation revealed that comprehensive healthcare measures targeted towards improved access to treatment, enhanced insecticide treated nets (ITN) compliance level, use of insecticide spray and reducing contact between human and mosquito are vital for controlling malaria prevalence.