Modeling of malaria transmission using delay differential equations

Abstract

Malaria is one of the major causes of deaths and ill health in endemic regions of sub- Saharan Africa and beyond despite efforts made to prevent and control its spread. Epidemiological models on how malaria is spread have made a substantial contribution on the understanding of disease changing aspects. Previous researchers have used Susceptible –Exposed-Infectious-Recovered (SEIR) model to explain how malaria is spread using ordinary differential equations. The main goal of this research was to develop mathematical SEIR epidemiology model to define the dynamics of the disease spread using delay differential equations with four control measures such as long lasting treated insecticides bed nets, intermittent preventive treatment of malaria in pregnant women (IPTP), intermittent preventive treatment of malaria in infancy (IPTI) and indoor residual spraying.The model would help health professionals to appreciate the dynamics of the spread of malaria and use the control measures above as intervention measures in controlling malaria spread. The model is then analysed and reproduction number derived using next generation matrix method and its stability is checked by jacobian matrix. Positivity of solutions and boundedness of the model is proved. We show that the disease free equilibrium is locally asymptotically stable if R0 < 1 and unstable if R0 > 1. Numerical simulations results shows that basic reproduction number R0 = 0:2004 and with proper treatment and control measures put in place the disease is controlled.