Individual-based Model (ibm): an Alternative Framework for Epidemiological Compartment Models

A traditional approach to model infectious diseases is to use compartment models based on differential equations, such as the SIR (Susceptible-Infected-Recovered) model. These models explain average behavior, but are inadequate to account for stochastic fluctuations of epidemiological variables. An alternative approach is to use Individual-Based Model (IBM), that represent each individual as a set of features that change dynamically over time. This allows modeling population phenomena as aggregates of individual interactions. This paper presents a general framework to model epidemiological systems using IBM as an alternative to replace or complement epidemiological compartment models. The proposed modeling approach is shown to allow the study of some phenomena which are related to finite-population demographic stochastic fluctuation. In particular, a procedure for the computation of the probability of disease eradication within a time horizon in the case of systems which have mean-field endemic equilibrium is presented as a direct application of the proposed approach. It is shown, how this general framework may be described as an algorithm suitable to model different types of compartment models. Numerical simulations illustrate how this approach may provide greater insight about a great variety of epidemiological systems.