This work is an extension of a previous publication. An optimal control
theory is applied to a model of malaria transmission dynamics to investigate
the control strategies for eliminating malaria using time dependent controls.
Four main efforts are considered including the treatment of infected humans,
the individual protection, vectors control strategies such as killing adult
anopheles and both aquatic stages and the implementation of an imperfect
vaccine which has already been tried in certain areas. The characterization of
the optimal control is carried out via the Pontryagin’s Maximum Principle
which shows the necessary conditions for controlling malaria. Numerical
simulations of the model show that restricted and proper use of control
measures might considerably decrease the size of mosquito population and
the number of infected among the human population accordingly.

mathematical modeling, malaria dynamics, optimal control, usual strategies, vaccination, Pontryagin’s Maximum Principle