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 intensiv e 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 commo n knowledge in literature that the disease can affect people of all ages, the mode of transmi ssion is still evasive. The studied model is expressed as a system of hyperbolic (first orde r) partial differential equations. We first, employ a representation from the method of charact eristics and a fixed point argument and also prove the existence and uniqueness of solutions to t he nonlinear system. We establish the mathematical well-posedness of the time evolution pr oblem 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.