Numerical Methods in Python for Solving Systems of Stochastic Differential Equations: An Application to the SIRD Model in Latin America

Author:

Quispe Dennis,Rubio Obidio

Abstract

In this chapter, we apply the exploration of the Euler–Maruyama, Milstein, and Runge–Kutta methods to solve systems of stochastic differential equations associated with the stochastic SIRD model. We simulate sample trajectories of each variable using Python and data collected in Peru during the years 2020 and 2021, marked by the onset of the COVID-19 pandemic. Our research involves comparing stochastic and deterministic systems obtained from the SIRD model in the Peruvian context. We use different values for the intensity of white noise to assess the impact of stochasticity on the dynamics of the SIRD model. Presenting random simulations alongside deterministic ones provides a comprehensive understanding of the effect of randomness in the context of infectious disease modeling.

Publisher

IntechOpen

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