Understanding the effects of individual awareness and vector controls on malaria transmission dynamics using multiple optimal control

Abstract

Malaria is a vector-borne diseases caused by parasite of genus Plasmodium and is transmitted via a bite of mosquitoes. Although the number of malaria cases has been reduced, an outbreak still happens, which causes deaths particularly in children. In this paper, mathematical models in the absence and presence of awareness programs and vector controls have been formulated and studied. The qualitative analysis of the model has been conducted. A global sensitivity analysis of the model has been performed to determine the most influential parameters on the increasing number of infected individuals and the reproduction number. An optimal control approach has been used to analyse the effects of control strategies and the model is fitted to data of malaria cases from Weeluri Health Center, Central Sumba, Indonesia. Qualitative analysis of the model showed that the disease-free and endemic equilibrium are globally stable. Furthermore, the reproduction number for malaria is found to be R0=1.1199. Results from global sensitivity analyses showed that the biting rate, the transmission probability from mosquitoes to human, and human to mosquitoes, and the number of mosquitoes per human are the most influential parameters, which indicate the importance of reducing the contact between human and mosquitoes. This suggests the awareness of individuals to take the prevention actions hold an important role for reducing the contact with mosquitoes. Furthermore, using the Pontryagin maximum principle, we found that the awareness programs and vector control should be implemented at a higher level and the vector controls need to be applied for the entire period to obtain the reduction in the number of infected individuals at the minimum costs. Interestingly, in the absence of vector control programs, it is still possible to reduce the number of malaria cases when the awareness programs have been implemented and aware individuals are willing to take the prevention actions.