Numerical treatment of optimal control theory applied to malaria transmission dynamic model

Abstract

Malaria is preventable and curable but critical disease caused by parasites that are transmitted to people through the bites of female Anopheles mosquitoes. There were an estimated 228 million cases of malaria globally and its mortality remained at 405,000 in 2018. There are many models that have been developed but the aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources. The authors in their previous work, developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. This model captured both the human and the mosquito compartments and considered 5 control interventions. Namely it was: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying with insecticide to reduce malaria transmission; insecticide treated net to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. In the present work we carried out basic mathematical analysis of the model, simulate the different scenarios developed and optimise the control interventions with optimal control. The potential of the control interventions to reduce transmission within 120 days was observed. The numerical experiments showed that the optimal strategy to effectively control malaria was through the combinations of controls in the models. The developed malaria model predicted the reduction, control and/or elimination of malaria threats through incorporating multiple control interventions. Therefore, multiple control measures should be adopted for malaria but in areas of limited resources, we can make use of strategy E and others in places where there are more resources.