Modeling and Transmission Dynamics of Leprosy Disease: Via Numerical Methods

Leprosy is a chronic infectious disease caused by Mycobacterium leprae, an acid-fast, rod-shaped bacillus. Leprosy is curable, and treatment in the early stages can prevent disability. In 2019, a total of 153 countries reported on leprosy to World Health Organization (WHO): 38 from the African region, 31 from the region of the Americas, 11 from the South-East Asia region, 19 from the Eastern Mediterranean region, 30 from the European region, and 24 from the Western Pacific region. In 2019, 0.2 million new cases of leprosy were detected, and the registered prevalence was 0.7 million cases. The population is categorized into four compartments such as susceptible (x), infected (y), paucibacillary leprosy (w), and multibacillary leprosy (z). The dynamics of disease are analyzed dynamically and numerically. The model predicts positivity, boundedness, equilibria, and local stability rigorously with the support of the reproduction number of the model. In numerical analysis, we develop some explicit and implicit models like Euler and Runge–Kutta methods are time-dependent and violate the physical relevance of the disease. Then, the proposed implicit way for the said model is independent of the time step size, dynamically consistent, positive, and bounded.