Mathematical model for analysing the interplay between income, nutrition, and tuberculosis dynamics

Abstract

This paper presents a mathematical framework to investigate the impact of socio-economic factors, specifically income and nutrition on the transmission dynamics of TB. Inadequate nutrition, driven by the unaffordability of a healthy diet in low and middle income countries, is a major barrier to achieve the WHO's End Tuberculosis (TB) strategy. To address this issue, the authors have developed a compartmental model by incorporating transmission rate β̃(M), recovery rate γ̃(N), and TB-related mortality rate μ̃_tb(N), as functions of income and nutrition levels. The model captures the dynamical interaction between these factors and their influence on disease spread, and mortality. In this work, the authors have calculated the reproduction number which quantifies the contagious nature of the disease by using next generation matrix approach and analysed its sensitivity using normalized forward sensitivity index approach. Through numerical simulations, the authors have analysed various scenarios such as including voluntary and mandatory nutrition uptake, as well as varying nutrition and income levels within the population. The results of the present model show that improved nutrition and higher income significantly reduce TB transmission and mortality, but the disease burden can only be fully alleviated when both factors are simultaneously addressed. The sensitivity analysis for the reproduction number highlights that reducing the transmission rate is essential for bringing the reproduction number R₀ below the crucial threshold of 1. This study emphasizes the necessity of holistic interventions that improve both nutrition and socio-economic conditions for effective TB control.

Keywords: Ecological modelling; Mathematical modelling; Poverty traps; Social epidemiology; Tuberculosis; Under nutrition.