Simulating Deterministic and Stochastic Models of Tuberculosis (TB) Transmission Dynamics
E. Jalija & O. Abu
Department of Mathematics and Statistics
Federal Polytechnic, Idah, Nigeria
Email: abuonoja2008@yahoo.com
Corresponding Author: O. Abu
ABSTRACT
In this paper, a stochastic differential equation model as a version of a deterministic model of tuberculosis transmission dynamics considering treatment rate and population density as controls is formulated. The objective of this study is to compare the solutions of both versions for varying areas. The two models were solved numerically using Runge-Kutta method of order four. The sample paths show different trends of TB disease spread and thus ensemble the variability inherent in the outcomes of the spread of disease observed in practice unlike the trajectory of the deterministic model that shows one outcome. This partly explains variability in global distribution of tuberculosis prevalence in communities with similar demographic and environmental factors. The findings of this study show that the role of chance effects on the spread of tuberculosis is significant.
Keywords: Tuberculosis, infection, stochastic model, deterministic model, chance effects
