Effect of Environmental Immunity on Mathematical Modeling of Malaria Transmission between Vector and Host Population

Abstract

The effect of environmental immunity on the mathematical modeling of malaria transmission between vector and host population is investigated in this study using appropriate standard procedures. We develop a mathematical SIR-SI model incorporating environmental immunity parameters to describe the dynamics transmission rates of both humans and vectors with the assumption that an individual develops environmental immunity on the infected and recovered classes. The model is analyzed by the reproduction number derived using the next-generation matrix method and its stability is checked by Jacobian matrix. We demonstrate that the disease-free equilibrium is locally asymptotically stable if ( – reproduction number) and is unstable if . Numerical simulation indicates that, with acquired environmental immunity due to nutrition and medicinal herbs, the spread of malaria can be significantly impacted by increasing the recovered class and lowering the infected class.