A Study of a Stochastic Model and Extinction Phenomenon of Meningitis Epidemic

Abstract

AbstractA stochastic version of the deterministic model for meningitis epidemic by Yaga and Saporu (2024) is developed. The stochastic mean system of equations for possible state of an individual in the model and the extinction probabilities for carrier and infective are derived. Comparison of the system of stochastic mean equations and its deterministic analogue of profiles for the various compartments and the case-carrier trajectories show similar pattern with a time shift difference. This indicates that there must be caution in using the deterministic analogue as an approximating system of the stochastic mean equations for inferential purpose. Simulation studies of the comparison of the compartmental profiles for the general case; model I, with the assumption that a proportion (φ ≠0), of the infected susceptible can move directly to the infective stage and that of the special case, model II, whenφ= 0 is examined for various values ofϵ(odds in favour of a carrier transmitting infection)≤2. It is only whenϵ= 2 that model II can approximate model I in all compartments except that of the carrier. Transmission rate,β, loss of carriership rate,σandϵare identified as the most sensitive parameters of the extinction probabilities. Threshold results derived for carrier and infective extinction probabilities are distinct but bear some relation, transmission rate required for carrier extinction is square of that for infective. It is concluded that carriership play a more prominent role in the transmission of meningitis epidemic and efforts aimed at control should be targeted at reducing the transmission rate and increasing the loss of carriership.