Abstract
In this note, we consider a compartmental epidemic mathematical model given by a system of differential equations. We provide a complete toolkit for performing both a symbolic and numerical analysis of the spreading of COVID-19. By using the free and open-source programming language Python and the mathematical software SageMath, we contribute for the reproducibility of the mathematical analysis of the stability of the equilibrium points of epidemic models and their fitting to real data. The mathematical tools and codes can be adapted to a wide range of mathematical epidemic models.
Highlights
Mathematical models for the transmission dynamics of infectious diseases have been a powerful tool to understand and control epidemics
We provided a complete toolkit for performing both a symbolic and numerical analysis of a recent epidemic model, presented in [25], introduced in order to study the spreading of the COVID19 pandemic
This innovative compartmental model takes into account the possible transmission of the virus by asymptomatic individuals, as well as the possibility to protect a fraction of the affected population by public health strategies, such as confinement or quarantine
Summary
Mathematical models for the transmission dynamics of infectious diseases have been a powerful tool to understand and control epidemics. SIR, SEIR, SEIRD-type models, among many others, have been used to analyze, predict and control the spread of SARS-CoV-2 virus worldwide, in what follows we refer to some of these models applied to COVID-19 given by systems of ODE’s. In the mathematical analysis of compartmental models given by systems of ODE’s, we may emphasize the stability analysis of the equilibrium points, the basic reproduction number and the model fitting to real data. We consider a SAIRP model, given by a system of five ODE’s, for the transmission of SARS-CoV-2, first proposed in [26] and after generalized to piecewise constant parameters and complex networks model in [25].
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