SEI3R2D2V: Pandemic Modeling and Analysis of Its Latent Factors: A Case Study of COVID-19 in India

For densely populated developing countries, such as India, where due to a lack of general and public awareness, limited data collection and compilation facilities, and inherent limitations of the available diagnostic test, accurate modeling of the pandemic is more challenging. Thus, a realistic model for predictions is required in order to formulate more effective strategic policies to control the COVID-19 pandemic using limited available resources. In this article, we propose a time-varying epidemiological model with two classes of compartments, reported and unreported, and consider influential latent factors, for example, undetectable infections, the false-negative rate of testing, testing hesitancy, vaccination efficacy, dual contact dynamics, and the possibility of reinfection in recovered as well as vaccinated individuals. For simulation purposes, we consider the COVID-19 data of India from March 13, 2020, to January 20, 2022. Furthermore, we provide a sensitivity analysis of various latent factors and predictions for the third wave in India. Simulated results suggest that India is able to control COVID-19 for the first time after the second wave, as observed from the trajectory of effective reproduction number. Moreover, for unseen or coming variants of virus for which vaccine efficacy is low, the available vaccine requires a high vaccination rate to control future waves.

Certain efficient techniques to solve the unreported cases of 2019−nCoV epidemic model

One of the furthermost intimidations that the death faced after the second World War is 2019-nCoV epidemic and most crucial large-scale health disaster of this century. We devote the current work to discuss the epidemic prediction for the epidemic model created for 2019-nCoV in Wuhan, China by certain approximate analytical methods such as differential transform method and variational iteration method. Further, we recognize unreported cases in numbers and the parameters of model are due to reported case data. For the considered system demonstrating the model of coronavirus, the series solution is conventional in the structure of the differential transform method. The obtained solutions are discussed in figures which show the performance of considered model. The results show that the used schemes are definite and trouble-free to execution for the system of nonlinear ODEs. The solutions exposed that the both schemes are in total agreement, correct and well-organized for solving systems of nonlinear differential equations. © 2022 Forum-Editrice Universitaria Udinese SRL. All rights reserved.

Modeling Vaccine Efficacy for COVID-19 Outbreak in New York City.

In this article we study the efficacy of vaccination in epidemiological reconstructions of COVID-19 epidemics from reported cases data. Given an epidemiological model, we developed in previous studies a method that allowed the computation of an instantaneous transmission rate that produced an exact fit of reported cases data of the COVID-19 outbreak. In this article, we improve the method by incorporating vaccination data. More precisely, we develop a model in which vaccination is variable in its effectiveness. We develop a new technique to compute the transmission rate in this model, which produces an exact fit to reported cases data, while quantifying the efficacy of the vaccine and the daily number of vaccinated. We apply our method to the reported cases data and vaccination data of New York City.

Real-Time Prediction of the End of an Epidemic Wave: COVID-19 in China as a Case-Study

Forecasting when an epidemic wave is likely to end is an important component of disease management, allowing deployment of limited control resources to be planned efficiently. Here, we report an analysis that we conducted in real-time during the first COVID-19 epidemic wave in mainland China. We developed a mathematical model to construct bounds on the end date of the first epidemic wave there, assuming that strong quarantine and testing measures remained in place until the epidemic wave was confirmed over. We used reported data on case numbers in China from January 20 to April 9, 2020. We first developed an analytic approach, obtaining a formula describing the probability distribution of the epidemic wave end date using a combination of deterministic modelling and the theory of continuous-time Markov processes. Then, we ran simulations of an individual-based model to demonstrate that our analytic predictions were accurate. We found that the predicted end date of the first epidemic wave in China depended on the proportion of infected individuals that are symptomatic and appear in case notification data, as opposed to remaining asymptomatic throughout their courses of infection. We therefore provide an easy-to-use approach for predicting the ends of epidemic waves, as well as a clear demonstration that predicted end-of-epidemic times depend on the extent of asymptomatic infection. Our framework can be applied to predict the ends of epidemic waves during future outbreaks of a wide range of pathogens. © 2022, Springer Nature Switzerland AG.

Mathematical Modelling of the Evolution Dynamics of the Coronavirus Disease 2019 (COVID-19) in Burkina Faso

In this paper, we develop a compartmental model of the COVID-19 epidemic in Burkina Faso by taking into account the compartments of hospitalized, severely hospitalized patients and dead persons. The model exhibits the traditional threshold behavior. We prove that when the basic reproduction number is less than one, the disease-free equilibrium is locally asymptotically stable. We use real data from Burkina Faso National Health Commission against COVID-19 to predict the dynamic of the disease and also the cumulative number of reported cases. We use public policies in our model in order to reduce the contact rate, and thereby to show how the reduction of daily reported infectious cases evolves with a view to assisting decision makers for a rapid treatment of the reported cases. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Using Unstated Cases to Correct for COVID-19 Pandemic Outbreak and Its Impact on Easing the Intervention for Qatar.

Epidemiological Modeling supports the evaluation of various disease management activities. The value of epidemiological models lies in their ability to study various scenarios and to provide governments with a priori knowledge of the consequence of disease incursions and the impact of preventive strategies. A prevalent method of modeling the spread of pandemics is to categorize individuals in the population as belonging to one of several distinct compartments, which represents their health status with regard to the pandemic. In this work, a modified SIR epidemic model is proposed and analyzed with respect to the identification of its parameters and initial values based on stated or recorded case data from public health sources to estimate the unreported cases and the effectiveness of public health policies such as social distancing in slowing the spread of the epidemic. The analysis aims to highlight the importance of unreported cases for correcting the underestimated basic reproduction number. In many epidemic outbreaks, the number of reported infections is likely much lower than the actual number of infections which can be calculated from the model's parameters derived from reported case data. The analysis is applied to the COVID-19 pandemic for several countries in the Gulf region and Europe.

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.

A mathematical model for COVID-19 transmission dynamics with a case study of India.

The ongoing COVID-19 has precipitated a major global crisis, with 968,117 total confirmed cases, 612,782 total recovered cases and 24,915 deaths in India as of July 15, 2020. In absence of any effective therapeutics or drugs and with an unknown epidemiological life cycle, predictive mathematical models can aid in understanding of both coronavirus disease control and management. In this study, we propose a compartmental mathematical model to predict and control the transmission dynamics of COVID-19 pandemic in India with epidemic data up to April 30, 2020. We compute the basic reproduction number R 0, which will be used further to study the model simulations and predictions. We perform local and global stability analysis for the infection free equilibrium point E 0 as well as an endemic equilibrium point E* with respect to the basic reproduction number R 0. Moreover, we showed the criteria of disease persistence for R 0 > 1. We conduct a sensitivity analysis in our coronavirus model to determine the relative importance of model parameters to disease transmission. We compute the sensitivity indices of the reproduction number R 0 (which quantifies initial disease transmission) to the estimated parameter values. For the estimated model parameters, we obtained R 0 = 1.6632 , which shows the substantial outbreak of COVID-19 in India. Our model simulation demonstrates that the disease transmission rate ßs is more effective to mitigate the basic reproduction number R 0. Based on estimated data, our model predict that about 60 days the peak will be higher for COVID-19 in India and after that the curve will plateau but the coronavirus diseases will persist for a long time.

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.