A Model for the Spread of Infectious Diseases with Application to COVID-19

Abstract

Given the present pandemic caused by the severe acute respiratory syndrome coronavirus 2 or SARS-CoV-2 virus, the authors tried fitting existing models for the daily loss of lives. Based on data reported by Worldometers on the initial stages (first wave) of the pandemic for countries acquiring the disease, the authors observed that the logarithmic rendering of their data hinted the response of a first-order process to a step function input, which may be modeled by a three-parameters function, as described in this paper. This model was compared against other similar, log(N)-class of models that are non-compartmental type (such as the susceptible, infected, and removed, or SIR models), obtaining good fit and statistical comparison results, where N denotes the cumulative number of daily presumed deaths. This simple first-order response model can also be applied to bacterial and other biological growth phenomena. Here we describe the model, the numerical methods utilized for its application to actual pandemic data, and the statistical comparisons with other models which shows that our simple model is comparatively outstanding, given its simplicity. While researching the models available, the authors found other functions that can also be applied, with extra parameters, to be described in follow-on articles.

Keywords

• epidemiology
• pandemic model
• contagious disease
• infectious disease model
• COVID-19
• mathematical models in epidemiology