Optimal control of malaria transmission dynamics combining some usual strategies and an imperfect vaccine

International audience 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.