Control of Tuberculosis epidemic in South Africa using a Multi-stage Stochastic Recourse approach for resource allocation under various transmission rates

Abstract

Tuberculosis (TB), caused by bacteria Mycobacterium tuberculosis, is one of the leading infectious diseases
globally. Every year, 10 million people fall ill with tuberculosis, and despite being a preventable and curable disease, TB
kills 1.5 million people every year. South Africa, as of 2022, is on WHO’s list of 30 countries with a high burden of
tuberculosis and has an incidence rate of 615 per 100,000. The TB epidemic has proliferated in South Africa due in part to
the HIV population. HIV is one of the most significant risk factors in TB spread. This is due to individuals with HIV having a
greater rate of active TB, meaning a greater chance of spreading the disease and a greater need for health resources.
While this connection between HIV and TB has significantly been researched, the implications on the budget for multiple
locations have not.This work presents a comprehensive multistage stochastic recourse method applied to an epidemic
compartmental model for TB dynamics. This model is analyzed for various TB transmission rates, taking into account
various biological, environmental, and socioeconomic factors in South Africa. The mathematical model incorporates the
progression from latent TB infection to active disease, accounting for variation in susceptibility, infectiousness, and
treatment responses. We employ discretized differential equations to describe the interaction between susceptible,
infected, and recovered populations, and incorporate stochastic transmission rates to capture the inherent randomness
in disease spread and intervention impacts. Sensitivity analyses identify key parameters influencing disease dynamics,
highlighting critical intervention points for effective TB control. Another contribution of this work involves the
development of a Graphical User Interface to allow users to input their own values and determine the effect of different
parameters on disease flow. Our results underscore the importance of early detection and targeted public health
strategies. The model serves as a robust tool for policymakers to simulate various scenarios and optimize TB control
measures, ultimately contributing to the global efforts in eradicating this enduring public health challenge.