Modeling and Optimal Control of Plasmodium Knowlesi Malaria Spread from Infected Humans to Mosquitoes
Mohammed Baba Abdullahi *
School of Mathematical Sciences Universiti Sains Malaysia (USM) 11 800 Penang, Malaysia.
Yahya Abu Hasan
School of Mathematical Sciences Universiti Sains Malaysia (USM) 11 800 Penang, Malaysia.
Farah Aini Abdullah
School of Mathematical Sciences Universiti Sains Malaysia (USM) 11 800 Penang, Malaysia.
*Author to whom correspondence should be addressed.
Abstract
Malaria as among vector-borne diseases is reemerging in areas where control efforts were once effective and emerging in areas though free of the disease as a consequence of human migration and rapid growth of international traffic from malaria prevalent areas of the world to malaria free zone. In this paper we develop a mathematical model for the spread of Plasmodium knowlesi malaria from infected humans to mosquitoes. The stability analysis of the model is investigated rigorously. The model is extended to assess the impact of time dependent preventive (biological and chemical control) against the mosquitoes and treatment for infected humans. The existence of optimal control is established analytically by the use of optimal control theory. Numerical simulations of the problem, suggest that applying the three control measure can effectively reduce if not eliminate the spread of Plasmodium knowlesi malaria in a community.
Keywords: Modeling, optimal control, infected humans, mosquitoes, Plasmodium knowlesi