Abstract
In this work, power-series solutions of compartmental epidemiological models are used to provide alternate methods to solve the corresponding systems of nonlinear differential equations. A simple and classical SIR compartmental model is considered to reveal clearly the idea of our approach. Moreover, a SAIRP compartmental model is also analyzed by using the same methodology, previously applied to the COVID-19 pandemic. Numerical experiments are performed to show the accuracy of this approach.
Highlights
Compartmental models have been intensively used to analyze and predict the evolution of diseases and pandemic
The population is divided in Susceptible, Infected and Recovered, giving rise to the SIR model analyzed by Kermack and McKendrick [2]
Very recently [24] a SAIRP model has been applied to analyze the evolution of the pandemic of COVID-19 in Portugal
Summary
Compartmental models have been intensively used to analyze and predict the evolution of diseases and pandemic. Some improvements have been presented in [4] These ideas have been used, e.g., to anticipate the number of necessary resources at intensive care units during the COVID-19 pandemic [5], by using compartmental mathematical models [6, 7], which consider fractional derivatives as (for example) in [8,9,10,11]. Many other works have considered compartmental models to analyze the spread of the pandemic of COVID-19. In this work we explore another approach to solve mathematical compartmental models, based on the power-series expansion of the solution of the differential system. We apply the main ideas to a recent compartmental model used to analyze the spread of the COVID-19 pandemic along with some numerical computations.
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