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1000
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Abstract/Summary
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Susceptible S-Infected I-Recovered R-Death D (SIRD) compartmental models are often used
for modelling of infectious diseases. On the basis of the analogy between SIRD and compartmental models in hydrology, this study makes mathematical formulations developed in
hydrology available for modelling in epidemiology. We adapt the Hayami model solution
of the diffusive wave equation generally used in hydrological modelling to compartmental
I–R–D models in epidemiology by simulating the relationships between the number of infectious I(t), the number of recoveries R(t) and the number of deaths D(t). The Hayami model is
easy-to-use, robust and parsimonious. We compare the empirical one-parameter exponential
model usually used in SIRD models to the two-parameter Hayami model. Applications were
implemented on the recent Covid-19 pandemic. The application on data from 24 countries
shows that both models give comparable performances for modelling the I–D relationship.
However, for modelling the I–R relationship and the active cases, the exponential model
gives fair performances whereas the Hayami model substantially improves the model performances. The Hayami model also presents the advantage that its parameters can be easily estimated from the analysis of the data distributions of I(t), R(t) and D(t). The Hayami model is
parsimonious with only two parameters which are useful to compare the temporal evolution
of recoveries and deaths in different countries based on different contamination rates and
recoveries strategies. This study highlights the interest of knowledge transfer between different
scientific disciplines in order to model different processes.
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