A study of a stochastic model and extinction phenomenon of meningitis epidemic

Samaila Jackson Yaga; Funmilayo W.O. Saporu

doi:10.1515/em-2024-0015

Article

A study of a stochastic model and extinction phenomenon of meningitis epidemic

Samaila Jackson Yaga and Funmilayo W.O. Saporu

Published/Copyright: January 29, 2025

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From the journal Epidemiologic Methods Volume 14 Issue 1

Abstract

Objectives

A stochastic version of the deterministic model for meningitis epidemic by Yaga and Saporu (A study of a deterministic model for meningitis epidemic. J Epidemiol Methods 2024;13:20230023) is developed.

Method

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.

Results

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, when φ=0 is examined for various values of ϵ (odds in favour of a carrier transmitting infection) ≤ 2 . It is only when ϵ=2 that model II can approximate model I in all compartments except that of the carrier. Transmission rate, β, loss of carriership rate, σ and ϵ are 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.

Conclusion

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.

Keywords: stochastic mean equation; simulation; extinction probability; sensitivity analysis; threshold conditions; case-carrier trajectories

Corresponding author: Samaila Jackson Yaga, Department of Statistics, University of Maiduguri, P.M.B 1069 Along Bama Road, 600211, Maiduguri, Borno, Nigeria; and Department of Statistics, University of Abuja, Abuja, Nigeria, E-mail: samailajyaga@unimaid.edu.ng

Samaila Jackson Yaga is a Visiting Scholar, Disease Dynamics Unit, University of Cambridge, Cambridge, United Kingdom.

Author contributions: All authors participated in the production of the manuscript from beginning to the end.
Research ethics: Not applicable.
Informed consent: Not applicable.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The authors state no conflict of interest.
Research funding: None declared.
Data availability: Not applicable.

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Received: 2024-05-04

Accepted: 2024-10-14

Published Online: 2025-01-29

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Articles in the same Issue

https://doi.org/10.1515/em-2024-0015

Keywords for this article

stochastic mean equation; simulation; extinction probability; sensitivity analysis; threshold conditions; case-carrier trajectories