Abstract
Until today, numerous models have been formulated to predict the spreading of Covid-19. Among them, the actively discussed susceptible-infected-removed (SIR) model is one of the most reliable. Unfortunately, many factors (i.e., social behaviors) can influence the outcomes as well as the occurrence of multiple contributions corresponding to multiple waves. Therefore, for a reliable evaluation of the conversion rates, data need to be continuously updated and analyzed. In this work, we propose a model using Gaussian functions, coming from the solution of an ordinary differential equation representing a logistic model, able to describe the growth rate of infected, deceased and recovered people in Italy. We correlate the Gaussian parameters with the number of people affected by COVID-19 as a function of the large-scale anti-contagion control measures strength, and also of vaccines effects adopted to reach herd immunity. The superposition of gaussian curves allow modeling the growth rate of the total cases, deceased and recovered people and reproducing the corresponding cumulative distribution and probability density functions. Moreover, we try to predict a time interval in which all people will be infected or vaccinated (with at least one dose) and/or the time end of pandemic in Italy when all people have been infected or vaccinated with two doses.
Highlights
To extract significant information from the epidemics data, we should perform a careful analysis of growth patterns in daily and total numbers of confirmed cases and deceases, looking for details about growth maxima positions and widths for both infected and deceased, and how they correlate with each other
The constant background assumption means that random contagion events are uniformly distributed in time regardless of the general epidemics data trend, in a consistent way with respect to the uncertainties and incompleteness of available data
The lag in the growth rate of deceased and recovered with respect to infected people is intrinsically included in the theory by means of the Gaussians centroid
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Mechanistic models based on differential equations, such as the well-known SIR model (Susceptible–Infectious–Recovered) and its numerous modifications, are the most used to mimic and predict the spread of COVID-19 by including specific assumptions on the chosen parameters which control transmission, disease, testing capacity and immunity [17,18,19,20] These models, on the contrary of crude statistical approaches, are able to consider nonlinear dependences such as the increasing diffusion speed with the number of infected people. In light of some measures currently in use to judge the lockdowns or to prevent spreading of the virus, Gaussian modelling provides exact and simple approximate relationships between the two relevant parameters of the function (peak time and width) This manuscript aims to discuss in detail the mutual relations between the growth rate of infected, deceased and recovered people as a function of the largescale anti-contagion control measures strength, and of vaccines effects adopted to reach herd immunity.
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