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Approximation of epidemics by inhomogeneous birth-and-death processes

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  • Clancy, Damian
  • O'Neill, Philip

Abstract

This paper is concerned with the approximation of a class of open population epidemic models by time-inhomogeneous birth-and-death processes. In particular, we consider models in which the population of susceptibles behaves in the absence of infection as a general branching process. It is shown that for a large initial number of susceptibles, the process of infectives behaves approximately as a time-inhomogeneous birth-and-death process. Strong convergence results are obtained over an increasing sequence of time intervals [0,tN], where N is the initial number of susceptibles and tN-->[infinity] as N-->[infinity].

Suggested Citation

  • Clancy, Damian & O'Neill, Philip, 1998. "Approximation of epidemics by inhomogeneous birth-and-death processes," Stochastic Processes and their Applications, Elsevier, vol. 73(2), pages 233-245, March.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:2:p:233-245
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    References listed on IDEAS

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    1. Ball, Frank & Donnelly, Peter, 1995. "Strong approximations for epidemic models," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 1-21, January.
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    Cited by:

    1. D. Clancy & P. D. O’Neill & P. K. Pollett, 2001. "Approximations for the Long-Term Behavior of an Open-Population Epidemic Model," Methodology and Computing in Applied Probability, Springer, vol. 3(1), pages 75-95, March.
    2. Barraza, Néstor Ruben & Pena, Gabriel & Moreno, Verónica, 2020. "A non-homogeneous Markov early epidemic growth dynamics model. Application to the SARS-CoV-2 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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