On Solving SDEs with linear coefficients and application to stochastic epidemic models

Year 2022, Volume: 6 Issue: 2, 280 - 286, 30.06.2022

Youssef El-khatib , Qasem Al-mdallal

https://doi.org/10.31197/atnaa.948300

Cited By: 2

Abstract

Stochastic Differential Equations (SDEs) are extensively utilized to model numerous physical quantities from
different fields. In particular, linear SDEs are used in epidemic modeling. It is crucial to ensure the positivity
of several quantities in an epidemic model. Numerous articles on this topic proves the positivity of SDEs
solutions using probabilistic tools, such as in Theorem 3.1 of [10]. In this work, we suggest an alternative
way to show the positivity of the solutions. The proposed approach is based on finding solutions to linear
SDEs using Itô formula. We comment on several examples of stochastic epidemic models existing in the
literature.

Keywords

epidemic models, stochastic differential equations, stochastic epidemic models.

Supporting Institution

United Arab Emirates University

Project Number

UPAR Grant No. 31S369

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