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

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.