Simulation of the behaviour of covid-19 with the stochastic SIRD model: case of Peru
DOI:
https://doi.org/10.17268/sel.mat.2023.01.08Keywords:
COVID-19 pandemic, deterministic and stochastic model, SIRD model, simulationAbstract
In this work, we simulate the dynamics of COVID-19 pandemic using a deterministic SIRD model and its stochastic SIRD model version. The model is used under a closed population of 32 625 984 from the peruvian country, where the coefficient of the transmission rate, the recovery rate, the dead rate and the initial condition are given for the data taken from the initial days reported by the first disease people in Peru.
References
Vergara, E. et al. Modelo básico epidemiológico SIR para el COVID-19: caso las Regiones del Perú. Selecciones Matemáticas. 2020; 7(1) 151:161.
Ministerio de Salud, Alerta Epidemiológica Código: AE-015-2020. Disponible en https://cdn.www.gob.pe/uploads/ document/file/582356/AE015.pdf.
El Koufi A, El Koufi N. Stochastic differential equation model of Covid-19: Case study of Pakistan. Results in Physics. 2022; 34:105218.
Jianhai Baoa, Xuerong Maob, Geroge Yinc, Chenggui Yuana. Competitive Lotka–Volterra population dynamics with jumps. Nonlinear Analysis. 2011; 74:6601–6616.
Gao H, Wang y. Stochastic mutualism model under regime switching with Lévy jumps. Physica A. 2019; 515:355-75.
Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. 1927; 115:700-721. Disponible en https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1927.0118.
INEI. PERÚ, Estimaciones y proyecciones de población por departamento, provincia y Distrito, 2018-2020. Edit. Digital. 2020. Disponible en https://proyectos.inei.gob.pe/Est/Lib0846.
Daqing J, Jiajia Y, Chunyan J, Ningzhong S. Asymptotic behavior of global positive solution to a stochastic SIR model. Math. and Comp. Modelling. 2011; 54:221–232.
Baccouch M, Temimi H, Ben-Romdhane M. A discontinuous Galerkin method for systems of stochastic differential equations with applications to population biology, finance, and physics. J. of Comput. and App. Math. 2021; 388:113297.
Rubio, O. La integral de lto y ecuaciones diferenciales estocásticas[Tesis de Maestria], Universidad Nacional de Ingeniería; Perú, 1990.
Zhou Y, Zhang W, Yuan S. Survival and stationary distribution of a SIR epidemic model with stochastic perturbations, Appl. Math. Comput. 2014; 244:118–131.
Desmond J. Higham. An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations. SIAM Review. 2001; 43(3):525-546.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
