Modelagem computacional espaço-temporal da disseminação da hanseníase

Abstract

Leprosy, also known as Hansen’s disease, is an infectious disease that mainly affects the skin and peripheral nerves and can cause permanent physical disabilities. The causative agent of the disease is the bacterium Mycobacterium leprae. Despite of the decrease in the number of leprosy cases in the world, the disease remains a global public concern, specially in some countries, such as Brazil, which did not achieve its reduction goal. This work aims to reproduce, using mathematical-computacional tools, the spread of leprosy cases in a two-dimensional domain, using for this purpose a compartmental SIR model. In SIR, compartments represent the groups of susceptible, infected and recovered individuals. In the model, the susceptible compartment is characterized by all individuals who are susceptible to the contagion of the disease or those who are bacillus resistent. The infected compartment is composed by all the infected individuals without, for simplification purposes, making differentiation between paucibacilar and multibacilar individuals. The spatio-temporal model was computationally solved using two distinct approaches. The first approach solved, in a deterministic way, the SIR system of equations using the finite difference method. The second approach solved the same system of equation in a stochastic way using for this purpose the Gillespie algorithm. The results were compared to, for validation purposes, the public health records database of Juiz de Fora, Brazil, which keeps the total number of leprosy cases in the city along time.