Abstract
In December 2019, a severe respiratory syndrome (COVID-19) caused by a new coronavirus (SARS-CoV-2) was identified in China and spread rapidly around the globe. COVID-19 was declared a pandemic by the World Health Organization (WHO) in March 2020. With eventually substantial global underestimation, more than 225 million cases were confirmed by the end of August 2021, counting more than 4.5 million deaths. COVID-19 symptoms range from mild (or no symptoms) to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and preexisting health conditions enhancing the risks of disease severity manifestation. In this paper, a mathematical model for COVID-19 transmission is proposed and analyzed. The model stratifies the studied population into two groups, older and younger. Applied to the COVID-19 outbreaks in Spain and in Italy, we find the disease-free equilibrium and the basic reproduction number for each case study. A sensitivity analysis to identify the key parameters which influence the basic reproduction number, and hence regulate the transmission dynamics of COVID-19, is also performed. Finally, the model is extended to its stochastic counterpart to encapsulate the variation or uncertainty found in the transmissibility of the disease. We observe the variability of the infectious population finding its distribution at a given time, demonstrating that for small populations, stochasticity will play an important role.
Highlights
The coronavirus pandemic and its emerging variants are currently a major global public health threat
COVID-19 symptoms can range from mild to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and preexisting health conditions enhancing risks of disease severity [2]
As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading
Summary
The coronavirus pandemic and its emerging variants are currently a major global public health threat. Globalisation has speeded up the spread of infections over a short period of time This has an impact on the public healthcare system and is detrimental to the economic development of many countries. As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Applied to the outbreaks in the Basque Country, Spain, a flexible framework was developed within the so-called COVID-19 Basque Modeling Task Force (BMTF). Over the course of the pandemic, a broad spectrum of research has been produced, e.g., statistical work using two common approaches, the SIR model and a log-linear model, analyzing the available empirical data and estimating the reproduction values for Spain and Italy countries [30].
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