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

Abstract

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