A mathematical model for the dynamics and MCMC analysis of tomato bacterial wilt disease

Abstract

In this paper, we formulate and analyze a mathematical model to investigate the transmission dynamics of tomato bacterial wilt disease (TBWD) in Mukono district, Uganda. We derive the basic reproduction number R0 and prove the existence of a diseasefree equilibrium point which is globally stable if R0 >1 and an endemic equilibrium which exists if R0 <1. Model parameters are estimated using the Markov Chain Monte Carlo (MCMC) methods and robustness tested. The model parameters were observed to be identifiable. Numerical simulations show that soil solarization and sensitization of farmers can help to eliminate the disease in Uganda. A modified tomato bacterial wilt model with control terms is formulated.