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Kermack-McKendrick epidemic model revisited

Josef Štěpán, Daniel Hlubinka (2007)

Kybernetika

This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale N t that solves the Engelbert–Schmidt stochastic differential equation (). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size N t . Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer...

Kermack-McKendrick epidemics vaccinated

Jakub Staněk (2008)

Kybernetika

This paper proposes a deterministic model for the spread of an epidemic. We extend the classical Kermack–McKendrick model, so that a more general contact rate is chosen and a vaccination added. The model is governed by a differential equation (DE) for the time dynamics of the susceptibles, infectives and removals subpopulation. We present some conditions on the existence and uniqueness of a solution to the nonlinear DE. The existence of limits and uniqueness of maximum of infected individuals are...

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