Monte Carlo simulation method in stability analysis of epidemiological models

Abstract

Differential equations are a very important tool for mathematical modeling to capture and describe dynamic processes in various disciplines. The most difficult challenge in differential equation-based modeling is determining the stability of the equilibrium point, especially for equilibria that cannot be found explicitly, which is usually the case in complex models with high dimensions. This paper presents an alternative method for analyzing the stability of an equilibrium point. The method presented is a numerical approach using Monte Carlo simulation. This stability analysis uses two different approaches, namely the stability ratio approach and the eigenvalue based analysis. Both approaches are tested on the SIR model whose stability has been tested. The model selected is one that can explicitly represent equilibrium. The aim is to validate the constructed method. The SIR model usually has a level of complexity in checking the stability of the internal equilibrium with the stability condition R₀>1. For parameters that allow human intervention in it, the influence of these parameters on the stability is studied. Therefore, in this numerical approach, it is necessary to build a stability domain of the interior equilibrium before implementing the Monte Carlo simulation. Simulation results show that both approaches are successful in approximating the interior equilibrium stability of epidemiological models.