Final size and partial distance estimate for a two-group SEIRD model.

In this paper we consider a SEIRD epidemic model for a population composed by two groups of individuals with asymmetric interaction. Given an approximate solution for the two-group model, we estimate the error of this approximation to the unknown solution to the second group based on the known error that the approximation has with respect to the solution to the first group. We also study the final size of the epidemic for each group. We illustrate our results with the spread of the coronavirus disease 2019 (COVID-19) pandemic in the New York County (USA) for the initial stage of the contamination, and in the cities of Petrolina and Juazeiro (Brazil).

Modified Predictor–Corrector Method for the Numerical Solution of a Fractional-Order SIR Model with 2019-nCoV

In this paper, we analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method. A compartmental model with four compartments, namely, susceptible, infected, reported and unreported, was adopted and modified to a new model incorporating fractional operators. In particular, by using a modified predictor–corrector method, we captured the nature of the obtained solution for different arbitrary orders. We investigated the influence of the fractional operator to present and discuss some interesting properties of the novel coronavirus infection. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Clarifying predictions for COVID-19 from testing data: The example of New York State.

With the spread of COVID-19 across the world, a large amount of data on reported cases has become available. We are studying here a potential bias induced by the daily number of tests which may be insufficient or vary over time. Indeed, tests are hard to produce at the early stage of the epidemic and can therefore be a limiting factor in the detection of cases. Such a limitation may have a strong impact on the reported cases data. Indeed, some cases may be missing from the official count because the number of tests was not sufficient on a given day. In this work, we propose a new differential equation epidemic model which uses the daily number of tests as an input. We obtain a good agreement between the model simulations and the reported cases data coming from the state of New York. We also explore the relationship between the dynamic of the number of tests and the dynamics of the cases. We obtain a good match between the data and the outcome of the model. Finally, by multiplying the number of tests by 2, 5, 10, and 100 we explore the consequences for the number of reported cases.

SI epidemic model applied to COVID-19 data in mainland China.

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit to the early cumulative data of SARS-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli-Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

Predicting the cumulative number of cases for the COVID-19 epidemic in China from early data.

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.

A new study of unreported cases of 2019-nCOV epidemic outbreaks.

2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom.

We model the COVID-19 coronavirus epidemics in China, South Korea, Italy, France, Germany and the United Kingdom. We identify the early phase of the epidemics, when the number of cases grows exponentially, before government implementation of major control measures. We identify the next phase of the epidemics, when these social measures result in a time-dependent exponentially decreasing number of cases. We use reported case data, both asymptomatic and symptomatic, to model the transmission dynamics. We also incorporate into the transmission dynamics unreported cases. We construct our models with comprehensive consideration of the identification of model parameters. A key feature of our model is the evaluation of the timing and magnitude of implementation of major public policies restricting social movement. We project forward in time the development of the epidemics in these countries based on our model analysis.

Unreported Cases for Age Dependent COVID-19 Outbreak in Japan.

We investigate the age structured data for the COVID-19 outbreak in Japan. We consider a mathematical model for the epidemic with unreported infectious patient with and without age structure. In particular, we build a new mathematical model and a new computational method to fit the data by using age classes dependent exponential growth at the early stage of the epidemic. This allows to take into account differences in the response of patients to the disease according to their age. This model also allows for a heterogeneous response of the population to the social distancing measures taken by the local government. We fit this model to the observed data and obtain a snapshot of the effective transmissions occurring inside the population at different times, which indicates where and among whom the disease propagates after the start of public mitigation measures.

A COVID-19 epidemic model with latency period.

At the beginning of a COVID-19 infection, there is a period of time known as the exposed or latency period, before an infected person is capable of transmitting the infection to another person. We develop two differential equations models to account for this period. The first is a model that incorporates infected persons in the exposed class, before transmission is possible. The second is a model that incorporates a time delay in infected persons, before transmission is possible. We apply both models to the COVID-19 epidemic in China. We estimate the epidemiological parameters in the models, such as the transmission rate and the basic reproductive number, using data of reported cases. We thus evaluate the role of the exposed or latency period in the dynamics of a COVID-19 epidemic.

Understanding Unreported Cases in the COVID-19 Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions.

We develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in Wuhan, China. We use reported case data up to 31 January 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model, we identify the number of unreported cases. We then use the model to project the epidemic forward with varying levels of public health interventions. The model predictions emphasize the importance of major public health interventions in controlling COVID-19 epidemics.