Vaccine efficacy for COVID-19 outbreak in New York City

This article aims to study the COVID-19 data for New York City. We use both the daily number of second does vaccination and the daily number of reported cases for New York City. This article provides a method to combine an epidemic model and such data. We explore the influence of vaccine efficacy on our results.

What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

BackgroundThe COVID-19 epidemic, which started in late December 2019 and rapidly spread throughout the world, was accompanied by an unprecedented release of reported case data. Our objective is to propose a fresh look at this data by coupling a phenomenological description to the epidemiological dynamics. MethodsWe use a phenomenological model to describe and regularize the data. This model can be matched by a single mathematical model reproducing the epidemiological dynamics with a time-dependent transmission rate. We provide a method to compute this transmission rate and reconstruct the changes in the social interactions between people as well as changes in host-pathogen interactions. This method is applied to the cumulative case data of 8 different geographic areas. FindingsWe reconstruct the transmission rate from the data, therefore we are in position to understand the contribution of the dynamical effects of social interactions (contacts between individuals) and the contribution of the dynamics of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important in the dynamic of COVID-19. We obtain an instantaneous reproduction number that stays below 3.5 from early beginning of the epidemic. ConclusionThe instantaneous reproduction number staying below 3.5 implies that it is sufficient to vaccinate 71% of the population in each state or country considered in our study. Therefore assuming the vaccines will remain efficient against the new variants, and to be more confident it is sufficient to vaccinate 75 - 80% to get rid of COVID-19 in each state or country. FundingThis research was funded by the Agence Nationale de la Recherche in France (Project name: MPCUII (PM) and (QG))

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 of 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.

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.

Estimating the last day for COVID-19 outbreak in mainland China

Our main aim is to estimate the end of the first wave epidemic of COVID-19 outbreak in mainland China. We developed mathematical models to predict reasonable bounds on the date of end of the COVID-19 epidemics in mainland China with strong quarantine and testing measures for a sufficiently long time. We used reported data in China from January 20, 2020 to April 9, 2020. We firstly used a deterministic approach to obtain a formula to compute the probability distribution of the extinction date by combining the models and continuous-time Markov processes. Then we present the individual based model (IMB) simulations to compare the result by deterministic approach and show the absolute difference between the estimated cumulative probability distribution computed by simulations and formula. We provide the predictions of the end of the first wave epidemic for different fractions f of asymptomatic infectious that become reported symptomatic infectious.