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An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique

Author

Listed:
  • Slama, Howida
  • Hussein, A.
  • El-Bedwhey, Nabila A.
  • Selim, Mustafa M.

Abstract

This paper adapts a multi-dimensional Random Variable Transformation technique to derive a comprehensive stochastic description of the Susceptible-Infected-Recovered epidemiological model. An approximate solution of a system of nonlinear differential equations, that characterizes this model, is deterministically obtained and, from this approximation, we derive the first probability density functions for the solution processes of susceptible, infected and recovered percentages. These probability density functions are used to find the approximate mean and variance functions, as well as the confidence intervals. Taking a general situation, the infection contact rate, the recovery rate and the initial conditions are taken to be random variables with arbitrary distributions. To test the validity of the theoretical findings associated to the proposed random epidemiological model, some numerical results are tabulated and graphically presented through an illustrative example.

Suggested Citation

  • Slama, Howida & Hussein, A. & El-Bedwhey, Nabila A. & Selim, Mustafa M., 2019. "An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 144-156.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:144-156
    DOI: 10.1016/j.amc.2019.05.019
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    References listed on IDEAS

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    1. Mingming Li & Xianning Liu, 2014. "An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    2. El-Wakil, S.A. & Sallah, M. & El-Hanbaly, A.M., 2015. "Random variable transformation for generalized stochastic radiative transfer in finite participating slab media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 66-79.
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    Cited by:

    1. Calatayud, Julia & Carlos Cortés, Juan & Jornet, Marc, 2020. "Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).

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