Mathematical modelling of meningitis serogroups A and C transmission in Sub-Saharan Africa: A case study in Ghana

Abstract

This study proposes an epidemiological model for Susceptible, Protected, Carriers (Men A and Men C), Infected (Men A and Men C) and Recovered (SPCIRS) to accurately estimate meningitis’ occurrence and transmission in Ghana. To validate this approach, reported data obtained by researchers on case studies in regions of Ghana that are part of the Sub-Saharan meningitis belt were used. Based on the model’s prediction, infected individuals have an equal probability of transmitting the infection to others through contact. Simulated results from the equilibrium-state analysis of this methodology reveal that there is a specific threshold parameter $\varsigma$ such that the disease-free equilibrium is globally asymptotically stable when $R_0<\varsigma \le 1$, whereas backward bifurcation occurs when $\varsigma <R_0\le 1$, in which case the disease-free equilibrium is unstable when $R_0>1$. A unique endemic equilibrium is present when $R_0$ is near 1, with the possibility of this equilibrium being locally asymptotically stable. Furthermore, the proposed model effectively fits the data from the examples studied. This highlighted the optimal control theory identifies ideal strategies for disease eradication and the impact of vaccination and treatment plans. When eradication is not feasible, Pontryagin’s Maximum Principle provides optimal disease management. It was deduced from the numerical simulations that high coverage of susceptible individuals receiving vaccinations, combined with the development of an efficient vaccine, is the best strategy for managing the bacteria.