Simulation of COVID-19 epidemic spread using Stochastic Differential Equations with Jump diffusion for SIR Model

Abstract

Mathematical epidemiology is one of the most important research areas, it has contributed to understanding the behavior and the impact also the prediction of infectious disease. One of the fundamental methods intended to see the behavior of the pandemic is the susceptible-infectious-recovered epidemic model. However, the deterministic approach of this model has some limitations in mathematical modeling, for that we propose to add a stochastic variation in SIR equations. In this paper we present a stochastic differential equation with jump-diffusion formula for COVID-19, then we estimate the parameters of our stochastic susceptible-infected-recovered model. Finally, we compare our result with real covid19 spread in Morocco.

Stochastic SIR model predicts the evolution of COVID-19 epidemics from public health and wastewater data in small and medium-sized municipalities: A one year study

“…Epidemiological compartmental deterministic models, like the Susceptible-Infected-Recovered (SIR) model firstly described by [5] (and extended versions of it) have been employed to predict COVID-19 spread [6] , [7] , [8] , [9] , [10] . However, predictability issues arise and models (whether they are phenomenological, mechanistic, or agent-based) are not efficient predict the COVID-19 pandemics in the long term [11] , [12] .…”

“…The unpredictable nature of the pandemic spread has been tackled, on the one hand from the perspective of deterministic chaos [14] , [15] , [16] and, on the other hand, using stochastic models [17] , [18] . Dynamic stochastic models for COVID-19 spread prediction can be broadly categorized into: (i) stochastic differential equations based in classical SIR models [8] , [17] , and (ii) compartmental models combined with Mote Carlo methods [6] , [19] , [20] , [21] .…”

Fractional stochastic calculus approach for evolution in time of epidemiological systems

“…The stochastic susceptible-infected-recovered (SIR) dynamics expressed using ordinary Itô-stochastic differential equation has been proposed in Refs. [27][28][29][30][31][32][33]. The statistical analysis described by the master equation and transition rates for the infection process was made in Ref.…”

Fractional Stochastic Differential Equation Approach for Spreading of Diseases

“…The stochastic susceptible-infected-recovered (SIR) dynamics expressed using an ordinary Itô-stochastic differential equation has been proposed in refs. [21][22][23][24][25][26][27]. The statistical analysis described by the master equation and transition rates for the infection process was made in ref.…”