MATHEMATICAL MODELLING FOR THE TRANSMISSION DYNAMICS OF RIFT VALLEY FEVER VIRUS WITH HUMAN HOST

Abstract

In this research, transmission dynamics of Rift Valley Fever (RVF) with mosquito, livestock and human host using ordinary differential equation was studied and analyzed. RVF is a viral zoonosis fundamentally transmitted by mosquitoes and primarily affects livestock but has the ability to affect humans. It has become a public worry due to its potential to spread rapidly and become an epidemic. The Effective Reproduction Number Rc was computed using next generation matrix and used to investigate the local and global stability of the equilibrium, the disease-free equilibrium state was found to be locally asymptotically stable if Rc< 1. And by constructing a function using Castillo-Chavez's method, the disease-free state is found to be globally asymptotically stable if 𝑅𝑐 ≤ 1. This implies that rift valley fever could be put under control in a population where the Reproduction Number is less than 1. Numerical simulations using Adomian Decomposition Method (ADM) gives insightful analytical results to further explore the dynamics of the disease.