Containing and Managing an Emerging Disease Outbreak: A Stochastic Modelling Approach.

21 Pages Posted: 15 Apr 2022

See all articles by Idriss Sekkak

Idriss Sekkak

Laboratory of PDE’s, Algebra and Spectral Geometry. Faculty of Sciences, Ibn Tofail University; Mathematics for Public Health, The Fields Institute for Research in Mathematical Sciences

Jude Dzevela Kong

Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), York University

Mohamed El Fatini

Laboratory of PDE’s, Algebra and Spectral Geometry. Faculty of Sciences, Ibn Tofail University,

Date Written: February 17, 2022

Abstract

The aim of this work is to design and analyze a novel stochastic model for an infectious disease transmission dynamics, that captures human responses to information about the disease, policy, and disease progression in the event of an outbreak. We design a behaviour-structured stochastic Susceptible-Infected-Quarantine-Recovered model incorporating a population logistic growth, non pharmaceutical interventions and a general functional response in order to capture respectively the long time growth of a population size, instant measures established by decision makers and human response behaviour. We carry out a thorough analysis to investigate the existence of the global and positive solutions and to explore the extinction and the persistence of the disease regarding the basic reproduction number of the model. Moreover, we use suitable Lyapunov functions and establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the stochastic SIQR model. In addition, we estimate the parameters of the model by fitting it to confirmed COVID-19 cases in Morocco using least squares method.

Note:
Funding Information: The author Idriss SEKKAK (Myself) is funded by The Mathematics for public health (MfPH) program at Fields Institute. This program is funded by NSERC-EIDM.

Conflict of Interests: None to declare.

Keywords: Stochastic process, Epidemic model, Extinction, Stationary distribution, Data fitting.

Suggested Citation

Sekkak, Idriss and Kong, Jude Dzevela and El Fatini, Mohamed, Containing and Managing an Emerging Disease Outbreak: A Stochastic Modelling Approach. (February 17, 2022). Available at SSRN: https://ssrn.com/abstract=4040246 or http://dx.doi.org/10.2139/ssrn.4040246

Idriss Sekkak (Contact Author)

Laboratory of PDE’s, Algebra and Spectral Geometry. Faculty of Sciences, Ibn Tofail University ( email )

Kenitra, 14000
Morocco

Mathematics for Public Health, The Fields Institute for Research in Mathematical Sciences ( email )

222 College Street, Second Floor
Toronto, Ontario M5T 3J1
Canada

Jude Dzevela Kong

Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), York University ( email )

4700 Keele St
Toronto, ON M3J 1P3
Canada

Mohamed El Fatini

Laboratory of PDE’s, Algebra and Spectral Geometry. Faculty of Sciences, Ibn Tofail University, ( email )

Communication & Cultural Studies
Morocco

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