Dynamical analysis and control strategies in modelling Ebola virus disease

Abstract

Abstract Ebola virus disease (EVD) is a severe infection with an extremely high fatality rate spread through direct and indirect contacts. Recently, an outbreak of EVD in West Africa brought public attention to this deadly disease. We study the spread of EVD through a two-patch model. We determine the basic reproduction number, the disease-free equilibrium, two boundary equilibria and the endemic equilibrium when the disease persists in the two sub-populations for specific conditions. Further, we introduce time-dependent controls into our proposed model. We analyse the optimal control problem where the control system is a mathematical model for EVD that incorporates educational campaigns. The control functions represent educational campaigns in their respective patches, with one patch having more effective controls than the other. We aim to study how these control measures would be implemented for a certain time period, in order to reduce or eliminate EVD in the respective communities, while minimising the intervention implementation costs. Numerical simulations results are provided to illustrate the dynamics of the disease in the presence of controls.