An Age-structured Model for the Spread of Buruli Ulcer: Analysis and Simulation in Ghana

Abstract

Despite the advances in medical research on its treatment and intensive public education on prevention and control, the Buruli ulcer (BU) continues to be a major public health problem that continues to overwhelm authorities in Ghana. Ghana is the second most endemic country after the Ivory Coast at the global level. While it is common knowledge in literature that the disease can affect people of all ages, the mode of transmission is still evasive. The studied model is expressed as a system of hyperbolic (first order) partial differential equations. We first, employ a representation from the method of characteristics and a fixed point argument and also prove the existence and uniqueness of solutions to the nonlinear system. We establish the mathematical well-posedness of the time evolution problem using the semigroup theory approach. We then determine the basic reproduction ratio R0. Then we present a numerical scheme to model the dynamics of BU. The simulation results showed that Mycobacterium ulcer has peak period of spread and reduced subsequently.