A Stochastic Model with Jumps for Smoking

Main Article Content

Mohamed Coulibaly
Modeste N'Zi

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.

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

Article Details

How to Cite
Coulibaly, M., & N’Zi, M. (2019). A Stochastic Model with Jumps for Smoking. Journal of Advances in Mathematics and Computer Science, 34(3-4), 1-16. https://doi.org/10.9734/jamcs/2019/v34i3-430207
Section
Original Research Article

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