We consider a global (location independent) model of pandemic growth which generalizes the SIR model to accommodate important features of the COVID-19 pandemic, notably the implementation of pandemic reduction measures. This "SHIR" model is applied to COVID-19 data, and shows promise as a simple, tractable formalism with few parameters that can be used to model pandemic case numbers. As an example we show that the average time dependence of new COVID-19 cases per day from 15 Central and Western European countries is in good agreement with the analytic, parameter-free prediction of the model
We present a simple technique to compare the development of the Covid-19 epidemic in different regions, based only on the time series of confirmed cases. Weekly new infections, taken for every day, are interpreted as infection potential of Covid-19. We derive a robust time-varying reproduction rate for the infection potential, including asymptomatic cases, which does not depend on death rate or testing intensity. It requires few assumptions and shows a more plausible time course than official reproduction rates in several countries.
The fatality rate of Covid-19 escalates with age and is larger in men than women. I show that these variations correlate strongly with the level of the viral receptor protein ACE2 in rat lungs, which is consistent with the still limited and apparently contradictory data on human ACE2. Surprisingly, lower levels of the receptor correlate with higher fatality. However, a previous mathematical model predicts that the speed of viral progression in the organism has a maximum and then declines with the receptor level. Moreover, many manifestations of severe CoViD-19, such as severe lung injury, exac…
An epidemiological model is developed for the spread of COVID-19 in South Africa. A variant of the classical compartmental SEIR model, called the SEIQRDP model, is used. As South Africa is still in the early phases of the global COVID-19 pandemic with the confirmed infectious cases not having peaked, the SEIQRDP model is first parameterized on data for Germany, Italy, and South Korea - countries for which the number of infectious cases are well past their peaks. Good fits are achieved with reasonable predictions of where the number of COVID-19 confirmed cases, deaths, and recovered cases will …
I employ a simple mathematical model of an epidemic process to evaluate how four basic quantities: the reproduction number (R), the numbers of sensitive (S) and infectious individuals(I), and total community size (N) affect strategies to control COVID-19. Numerical simulations show that strict suppression measures at the beginning of an epidemic can create low infectious numbers, which thereafter can be managed by mitigation measures over longer periods to flatten the epidemic curve. The stronger the suppression measure, the faster it achieves the low numbers of infections that are conducive t…
On the base of logic discrete equations system mathematical modeling of COVID-19 epidemic spread was carried out in the world and in the countries with the largest number of infected people such as the USA, Brasil, Russia and India in the first half of 2020. It was shown that for the countries with strong restrictive measures the spread of COVID-19 fit on a single wave with small capacity as for a number of countries with violation of restrictive measures the spread of the epidemic fit on a waves superposition. For countries with large population mixing, the spread of the epidemic today also f…
The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the re…
While COVID-19 is rapidly propagating around the globe, the need for providing real-time forecasts of the epidemics pushes fits of dynamical and statistical models to available data beyond their capabilities. Here we focus on statistical predictions of COVID-19 infections performed by fitting asymptotic distributions to actual data. By taking as a case-study the epidemic evolution of total COVID-19 infections in Chinese provinces and Italian regions, we find that predictions are characterized by large uncertainties at the early stages of the epidemic growth. Those uncertainties significantly r…
The spread of the coronavirus (COVID-19), starting in late 2019, has determined in Italy several interventions aimed to prevent saturation of the health system. We have examined the effects of such measures by proposing a mean-field model describing the spread of the infection based on a simple diffusion process where all the observable variables (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely diffusion coefficient, infection cross-section, and…
We have further extended our compartmental model describing the spread of the infection in Italy. The model is based on the assumption that the time evolution of all of the observable quantities (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely people diffusion coefficient, infection cross-section, and population density. The model provides precious information on the tight relationship between the variation of the reported infection cases and a …
Successful predictive modeling of epidemics requires an understanding of the implicit feedback control strategies which are implemented by populations to modulate the spread of contagion. While this task of capturing endogenous behavior can be achieved through intricate modeling assumptions, we find that a population's reaction to case counts can be described through a second order affine dynamical system with linear control which fits well to the data across different regions and times throughout the COVID-19 pandemic. The model fits the data well both in and out of sample across the 50 state…
Data assimilation is used to optimally fit a classical epidemiology model to the Johns Hopkins data of the Covid-19 pandemic. The optimisation is based on the confirmed cases and confirmed deaths. This is the only data available with reasonable accuracy. Infection and recovery rates can be infered from the model as well as the model parameters. The parameters can be linked with government actions or events like the end of the holiday season. Based on this numbers predictions for the future can be made and control targets specified. With other words: We look for a solution to a given model whic…
A mathematical model of COVID-19 with minimal compartments is developed. The model is simple enough to fit data on confirmed cases, estimate the hidden infection figure and incorporate the effect of vaccination. With the effect of the new variant being considered, the model fits well with Philippine data of confirmed cases. With the fitted parameters, results show that a second peak, strikingly similar in magnitude to the first, is to be expected if the current transmission rate is increased by about 5\% and already a complete disaster if it will go up to 20\%. The model is then used to estima…
The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, sub-exponential increase of confirmed cases during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak with sufficiently large reproduction rate. Although case counts vary significantly between affected provinces in Mainland China, the scaling law $t^μ$ is surprisingly universal, with a range of exponents $μ=2.1\pm0.3$. The universality of this behavior indicates that despite social, regional, demographical, geographical, and socio-economi…
In this work, we adapt the epidemiological SIR model to study the evolution of the dissemination of COVID-19 in Germany and Brazil (nationally, in the State of Paraiba, and in the City of Campina Grande). We prove the well posedness and the continuous dependence of the model dynamics on its parameters. We also propose a simple probabilistic method for the evolution of the active cases that is instrumental for the automatic estimation of parameters of the epidemiological model. We obtained statistical estimates of the active cases based the probabilistic method and on the confirmed cases data. …
We consider the pandemic spreading of COVID-19 for some selected countries after the outbreak of the coronavirus in Wuhan City, China. We estimated the infection rate and the initial infected individuals of COVID-19 by using the officially reported data at the early stage of the epidemic for the susceptible (S), infectable (I), quarantined (Q), and the cofirmed recovered (Rk) population model, so called SIQRk model. In the reported data we know the quarantined cases and the recovered cases. We can not know the recovered cases from the asymptomatic cases. In the SIQRk model we can estimated the…
Non-pharmaceutical interventions (NPIs) such as quarantine, self-isolation, social distancing, and virus-contact tracing can greatly reduce the spread of the virus during a pandemic. In the wave of the COVID-19 pandemic, many countries have implemented various NPIs for infection control and mitigation. However, the stringency of the NPIs and the resulting impact among different countries remain unclear due to the lack of quantitative factors. In this study we took a further step to incorporate the effect of the NPIs into the pandemic dynamics model using the concept of policy intensity factor …
This paper has a twofold contribution. The first is a data driven approach for predicting the Covid 19 pandemic dynamics, based on data from more advanced countries. The second is to report and discuss the results obtained with this approach for Brazilian states, as of May 4th, 2020. We start by presenting preliminary results obtained by training an LSTM SAE network, which are somewhat disappointing. Then, our main approach consists in an initial clustering of the world regions for which data is available and where the pandemic is at an advanced stage, based on a set of manually engineered fea…
During the COVID-19 pandemic, the scientific community developed predictive models to evaluate potential governmental interventions. However, the analysis of the effects these interventions had is less advanced. Here, we propose a data-driven framework to assess these effects retrospectively. We use a regularized regression to find a parsimonious model that fits the data with the least changes in the Rt parameter. Then, we postulate each jump in Rt as the effect of an intervention. Following the do-operator prescriptions, we simulate the counterfactual case by forcing Rt to stay at the pre-jum…
In this work, we discuss the SIR epidemiological model and different variations of it applied to the propagation of the COVID-19 pandemia; we employ the data of the state of Guanajuato and of Mexico. We present some considerations that can improve the predictions made by those models. We consider a time-dependent infection rate, which we adjust to the data. Starting from a linear regime where the populations are much smaller that the country or state population and the population of susceptible (S) can be approximated in convenient units to S approximately 1, we make fits of the parameters. We…
A simple analytical model for modeling the evolution of the 2020 COVID-19 pandemic is presented. The model is based on the numerical solution of the widely used Susceptible-Infectious-Removed (SIR) populations model for describing epidemics. We consider an expanded version of the original Kermack-McKendrick model, which includes a decaying value of the parameter $β$ (the effective contact rate) due to externally imposed conditions, to which we refer as the forced-SIR (FSIR) model. We introduce an approximate analytical solution to the differential equations that represent the FSIR model which …
Non-pharmaceutical interventions(NPIs) play an important role in the early stage control of COVID-19 pandemic. Vaccination is considered to be the inevitable course to stop the spread of SARS-CoV-2. Based on the mechanism, a SVEIR COVID-19 model with vaccination and NPIs is proposed. By means of the basic reproduction number $R_{0}$, it is shown that the disease-free equilibrium is globally attractive if $\mathscr{R}_{0}<1$, and COVID-19 is uniform persistence if $\mathscr{R}_{0}>1$. Taking Indian dates for example in the numerical simulation, we find that our dynamical results fits well with …
In this paper, we propose a new real-time differential virus transmission model, which can give more accurate and robust short-term predictions of COVID-19 transmitted infectious disease with benefits of near-term trend projection. Different from the existing Susceptible-Exposed-Infected-Removed (SEIR) based virus transmission models, which fits well for pandemic modeling with sufficient historical data, the new model, which is also SEIR based, uses short history data to find the trend of the changing disease dynamics for the infected, the dead and the recovered so that it can naturally accomm…
The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Giuseppe Gaeta, arXiv:2003.08720 [q-bio.PE] (2020). In this paper we investigate a slightly generalized version of the same model and propose a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals. The scheme is…
We discovered that the time evolution of the inverse fractional daily growth of new infections, N/dN, in the current outbreak of COVID-19 is accurately described by a universal function, namely the two-parameter Gumbel cumulative function, in all countries that we have investigated. While the two Gumbel parameters, as determined bit fits to the data, vary from country to country (and even within different regions of the same country), reflecting the diversity and efficacy of the adopted containment measures, the functional form of the evolution of N/dN appears to be universal. The result of th…
