Shigellosis Dynamics: Modelling the Effects of Treatment, Sanitation, and Education in the Presence of Carriers - Stephen Edward; Eunice Mureithi; Nyimvua Shaban (International Journal of Mathematics and Mathematical Sciences)
A mathematical model for Shigellosis including disease carriers with multiple control strategies is developed. We compute the effective reproductive number Re, which is used to analyze the local stability of the equilibria, while the comparison theorem is used to prove global stability. By constructing a suitable Lyapunov function, the model endemic equilibrium is globally asymptotically stable when Re>1. Sensitivity analysis is performed to investigate the parameters that have a high impact on the transmission dynamics of the disease with direct transmission contributing more infections than indirect transmission. The effects of control measures are then investigated both analytically and numerically. Numerical results show that there is a reduction in the number of infections when at least a single control measure is applied efficiently. However, as the number of control interventions increases, Shigellosis elimination is more possible. Results also show that carriers play a potential role in the prevalence of Shigellosis and ignoring these individuals could potentially undermine the efforts of containing this epidemic.