A Stochastic Approach of SIRC Model Using Individual-Based Epidemiological Models

Abstract

Mathematical models are important instruments in epidemiology to assist in analyzing epidemiological dynamics as well as possible dissemination controls. Classical model uses differential equations to describe dynamics of population over time. A widely used example is susceptible-infected-recovered (SIR) compartmental model. Such model has been used to obtain optimum control policies in different scenarios. This model has been enhanced to include dynamics of reinfection of disease including a new compartment, known as susceptible-infected-recovered-cross-immune (SIRC). An alternative model is to consider each individual as a string or vector of characteristic data and simulate the contagion and recovery processes by computational means. This type of model, referred in literature as individual based model (IBM) has advantage of being flexible as characteristics of each individual can be quite complex, involving, for instance, age, sex, pre-existing health conditions, environmental factors, social, and habits. However, it was not found in literature equivalence in an IBM model for SIRC model. Some works have shown the possibility of equivalence between IBM and SIR models, in order to simulate similar scenarios with models of different natures, in deterministic and stochastic case respectively. In this context, this work proposes implementation of an IBM stochastic model equivalent to SIRC model. Results show that equivalence is also possible only with the proper configuration of parameters of IBM model. Accuracy of equivalent model showed better with reduction of time step end increase the size of population.