Department of Mathematics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia; Department of Mathematics, Faculty of Science and technology, University of Sultane Moulay Slimane, B.P. 523, Beni-Mellal, Morocco

Kassa, S.M., Department of Mathematics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia; Ouhinou, A., Department of Mathematics, Faculty of Science and technology, University of Sultane Moulay Slimane, B.P. 523, Beni-Mellal, Morocco

A mathematical model for infectious disease epidemics with behaviour change and treatment is formulated and analysed. It is indicated that behaviour modification by the population has a significant impact on the dynamics of the disease. Moreover, an optimal control theory is applied to propose the best possible combination of efforts in controlling a disease. It is shown that it may not be necessary to continuously apply treatment at a full rate to eradicate the disease, if the effort is supported by effective behaviour modification strategies. © 2014, Springer-Verlag Berlin Heidelberg.

behavior therapy; biological model; Botswana; Communicable Diseases; computer simulation; Epidemics; health behavior; HIV Infections; human; infection control; mathematical phenomena; procedures; psychology; public health service; statistical model; statistics and numerical data; transmission; Behavior Therapy; Botswana; Communicable Diseases; Computer Simulation; Epidemics; Health Behavior; HIV Infections; Humans; Infection Control; Mathematical Concepts; Models, Biological; Models, Statistical; Public Health Practice