On Solving SDEs with linear coefficients and application to stochastic epidemic models
- 30 June 2022
- journal article
- Published by Erdal Karapinar in Advances in the Theory of Nonlinear Analysis and its Application
- Vol. 6 (2), 280-286
- https://doi.org/10.31197/atnaa.948300
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.Keywords
Funding Information
- United Arab Emirates University (UPAR Grant No. 31S369)
This publication has 14 references indexed in Scilit:
- Dynamics of a stochastic SICA epidemic model for HIV transmission with higher-order perturbationStochastic Analysis and Applications, 2021
- Analysis of exact solution of stochastic sex-structured HIV/AIDS epidemic model with effect of screening of infectivesMathematics and Computers in Simulation, 2020
- Numerical techniques for stochastic foot and mouth disease epidemic model with the impact of vaccinationAdvances in Difference Equations, 2020
- A stochastic SICA epidemic model for HIV transmissionApplied Mathematics Letters, 2018
- The role of power decay, exponential decay and Mittag-Leffler function’s waiting time distribution: Application of cancer spreadPhysica A: Statistical Mechanics and its Applications, 2018
- A new numerical approximation of the fractal ordinary differential equationThe European Physical Journal Plus, 2018
- Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth methodThe European Physical Journal Plus, 2018
- Dynamical behaviors of a stochastic SIRI epidemic modelApplicable Analysis, 2016
- SIVR epidemic model with stochastic perturbationNeural Computing & Applications, 2012
- Numerical Solution of Stochastic Differential EquationsPublished by Springer Science and Business Media LLC ,1992