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A COVID-19 time-dependent SIRD model using functional differential equations
Edson A. Coayla-Teran
In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19) with the goal to do forecasts for the number of infected, recovered and deceased individuals. To do this, we propose a SIRD model, which takes into account the fact that susceptible individuals that meet infected individuals are not immediately infected, they become infected after a period. Similarly, infected individuals recovered or deceased not immediately but after a period which is denoted. These considerations produce discrete delays in the classic SIRD model which is a particular case of functional differential equations. Furthermore, to take into account the effect of the social distancing, mask use or other actions to reduce the risk of infectivity, we consider that the transmission, the recovery and the death rates are not constants but time-dependent. To apply the model proposed, we developed an algorithm which uses ridge regression to do forecasts for the Peruvian regions of Moquegua and Tacna.
Covid-19, SIRD model, Functional differential equations, Ridge regression.
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