Impact of local and global awareness campaigns on malaria transmission: A mathematical model with protected human class and optimal control approach

Abstract

This article presents a mathematical model to study malaria transmission dynamics influenced by awareness campaigns and optimal control strategies. Protected human class is included as a model variable that can be increased by social media awareness and treatment, as a result, infected cases are reduced. The nonnegativity and boundedness of the solutions of the model are analyzed. The proposed model possesses two equilibria, namely the disease-free equilibrium and the endemic equilibrium point. The disease-free equilibrium point is stable when the basic reproduction number, \({\mathcal {R}}_0<1\) and endemic equilibrium exists when \({\mathcal {R}}_0>1\). Consequently, forward bifurcation occurs at \({\mathcal {R}}_0=1\). Sensitivity analysis is provided which identifies the more important parameters of the model system related to the disease transmission. Finally, optimal control theory has been applied to maximize the number of protected human and minimize the cost of malaria management. The optimal problem comprises of three control parameters, and it is solved using the ‘maximum principle.’ This study concluded that public awareness is important for malaria control, and a combination of awareness-based interventions such as use of bed nets, spraying insecticides, and treatment can optimally increase the protected human as well as minimize the malaria cases cost-effectively.