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Exact solutions and analysis of an SIR variant with constant-time recovery

Abstract : We investigate a variant of the SIR epidemiological model in which the recovery of infected individuals takes place in constant time rather than following an exponential distribution. This model is described by a delay-differential equation: we show that the equations in question admit an exact solution in closed form (given by rational functions of an exponential of time). Using this, we investigate the qualitative differences between this modified model and classical SIR and show that, for the same reproduction number, contagiousness and expected recovery time, the constant-time recovery variant entails a sharper, more pronounced, epidemiological peak than the classical variant (exponential-process recovery), while still having the same final attack rate.
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Contributor : David Madore Connect in order to contact the contributor
Submitted on : Wednesday, April 8, 2020 - 5:31:29 PM
Last modification on : Monday, January 24, 2022 - 8:26:30 AM


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  • HAL Id : hal-02537265, version 1



David Alexander Madore. Exact solutions and analysis of an SIR variant with constant-time recovery. 2020. ⟨hal-02537265⟩



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