MODELLING LATENT INFECTED DYNAMICS IN TUBERCULOSIS SPREAD IN INDIAN CONTEXT

Abstract

Tuberculosis (TB) is an infectious disease caused by the bacterium Mycobacterium tuberculosis. While it predominantly affects the lungs, it can also affect other organs, including the kidneys, spine, and brain. The bacteria spreads through airborne droplets expelled when an infected person coughs, sneezes, or talks. Many individuals who contract the bacteria might also develop a latent TB infection, during which the bacteria remains dormant and non-contagious. However, some may progress to active TB, characterized by symptoms such as a persistent cough, chest pain, coughing up blood, fatigue, weight loss, fever, and night sweats. Early diagnosis and treatment is essential for curing the disease and preventing transmission.

Despite medical advancements, TB remains a significant global health concern, particularly in low and middle income countries. In 2020, TB affected approximately 10 million people worldwide, resulting in 1.5 million deaths, positioning it as one of the leading causes of mortality [1][2]. The emergence of drug-resistant strains, such as multi-drug-resistant TB (MDR-TB) and extensively drug-resistant TB (XDR-TB), poses additional challenges for TB control. Key preventive measures include early detection and treatment, vaccination with Bacillus Calmette Guerin (BCG), and addressing social determinants of health. The World Health Organization (WHO) has set ambitious targets to reduce TB incidence and mortality, aiming to end the global TB epidemic by 2030, as outlined in the Sustainable Development Goals (SDGs) [3][4][5].

Compartmental models are a fundamental approach in mathematical modelling, particularly useful in epidemiology for studying the spread of infectious diseases. These models divide the population into distinct compartments based on disease status, such as susceptible, exposed, infected, and recovered individuals. By using differential equations to describe the rates of movement between compartments, we can study how diseases propagate through populations over time. Mathematical models are invaluable in understanding TB dynamics and shaping public health strategies. This paper introduces a mathematical model for TB that incorporates the latent TB component, offering a more comprehensive view of TB transmission dynamics with respect to India.