Simple Mathematical Model for Malaria Transmission
Mojeeb AL-Rahman EL-Nor Osman *
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China and Department of Mathematics and Computer Science, International University of Africa, P.O.Box 2469, Khartoum, Sudan.
Isaac Kwasi Adu
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China and Department of Mathematics, Valley View University, Techiman Campus, P.O.Box 183 B/A, Ghana.
*Author to whom correspondence should be addressed.
Abstract
Our model is made up of two sections: In the first section, we study a simple SEIR model, estimated the reproduction number, discussed the disease-free and endemic equilibria using the Routh-Hurwitz criterion and second additive compound matrix respectively. A global stability of disease-free and the endemic equilibria was performed using Lasselle’s invariance principle of Lyapunov functions. In the second section of our model, we considered SEIR-SEI model of malaria transmission between humans and mosquitoes. We estimated the reproduction number and discussed the stability of the disease-free and endemic equilibria. The disease-free equilibrium was locally asymptotically stable if the reproduction number is less than one and unstable if the reproduction number is greater than one in both models. Numerical simulations were conducted using Matlab software to confirm our analytic results. Our findings were that, Malaria may be controlled by reducing the contact rate between human and mosquito, the use of active malaria drugs, insecticides and mosquito treated nets can also help to reduce mosquitoes population and malaria transmission respectively.
Keywords: Mathematical model, disease-free equilibrium, endemic equilibrium, Lyapunov function, locally asymptotically stable.