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Research Article Open access CC BY 4.0

A Stochastic Model with Jumps for Smoking

Coulibaly Mohamed, N'Zi Modeste, Mohamed Coulibaly, Modeste N'zi

Journal of Advances in Mathematics and Computer Science · pp. 1–16 · Published 1 Nov 2019

10.9734/jamcs/2019/v34i3-430207

Abstract

Some stochastic epidemiological models are less significant. They do not take into account some sudden events that could disrupt the behavior of the studied phenomenon. In this work, we introduce a white noise and jumps in a deterministic SIRS model for smoking to take into account of the effects of randomly fluctuation and such sudden factors respectively. First of all we prove that the solution of the stochastic differential equation with jumps of the new model is positive. Then we study the asymptotic behavior around the smoking-free equilibrium state and the smoking-present equilibrium state of the original deterministic model. Under certain conditions, we show that the solution oscillate respectively around these equilibrium states. We prove that the intensity of these oscillations depends on the magnitude of noise and the jump diffusion coefficient of our stochastic differential equation with jumps. To support our theoretical results, we realise numerical simulations. The observations confirm our conclusions.

Smoking model jump perturbation global positive solution asymptotic behavior numerical simulation.

Cited by 6

A Susceptible Vaccinated Exposed Infected Hospitalized and Removed/Recovered (SVEIHR) Model Framework for COVID-19

S.O. Oyamakin, J.I Popoola · 2023

A stochastic model with jumps for smoking incorporating media coverage

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