Estimating epidemic parameters: Application to H1N1 pandemic data

Dynamic SARS-CoV-2 surveillance model combining seroprevalence and wastewater concentrations for post-vaccine disease burden estimates

BACKGROUND

Despite wide scale assessments, it remains unclear how large-scale severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccination affected the wastewater concentration of the virus or the overall disease burden as measured by hospitalization rates.

METHODS

We used weekly SARS-CoV-2 wastewater concentration with a stratified random sampling of seroprevalence, and linked vaccination and hospitalization data, from April 2021-August 2021 in Jefferson County, Kentucky (USA). Our susceptible ( S ), vaccinated ( V ), variant-specific infected (I 1 andI 2 ), recovered ( R ), and seropositive ( T ) model ( S V I 2 R T ) tracked prevalence longitudinally. This was related to wastewater concentration.

RESULTS

Here we show the 64% county vaccination rate translate into about a 61% decrease in SARS-CoV-2 incidence. The estimated effect of SARS-CoV-2 Delta variant emergence is a 24-fold increase of infection counts, which correspond to an over 9-fold increase in wastewater concentration. Hospitalization burden and wastewater concentration have the strongest correlation (r = 0.95) at 1 week lag.

CONCLUSIONS

Our study underscores the importance of continuing environmental surveillance post-vaccine and provides a proof-of-concept for environmental epidemiology monitoring of infectious disease for future pandemic preparedness.

Incidence rate drive the multiple wave in the COVID-19 pandemic

The last three years have been the most challenging for humanity due to the COVID-19 pandemic. The novel viral infection has eventually been able to infect most of the human population. It is now considered to be in the endemic stage, meaning it will remain in our world throughout our lifetime. There will be an intermittent outbreak of the COVID infection from time to time. Therefore, it is necessary to formulate a robust Mathematical model to study the dynamics of disease to have a control mechanism in place. In this article, we suggest a modified MSEIR model to explain the dynamics of COVID-19 infection. We assume that a susceptible person contracting the coronavirus develops a transient immunity to the illness. Further, infectives comprise asymptomatic, symptomatic, hospitalized and quarantined individuals. We assume that the incidence rate is of standard type, and susceptible can only become infective if they come in contact with either asymptomatic or symptomatic individuals. This basic and simple model effectively models the various waves every country has seen during the Pandemic. The simple analysis shows that the model could suggest various waves in future if we carefully select the incidence rate for the infection. In summary, we have discussed the following major points in this article. •We have analysed for local behavior infection-free equilibrium solution. Further, a thorough numerical exploration with various parameter settings has been performed to obtain the different cases of infection dynamics of the coronavirus epidemic.•We have found some interesting scenarios which explain the emergence of multiple waves observed in many countries.

Generalized SIR (GSIR) epidemic model: An improved framework for the predictive monitoring of COVID-19 pandemic

Novel coronavirus respiratory disease COVID-19 has caused havoc in many countries across the globe. In order to contain infection of this highly contagious disease, most of the world population is constrained to live in a complete or partial lockdown for months together with a minimal human-to-human interaction having far reaching consequences on countries' economy and mental well-being of their citizens. Hence, there is a need for a good predictive model for the health advisory bodies and decision makers for taking calculated proactive measures to contain the pandemic and maintain a healthy economy. This paper extends the mathematical theory of the classical Susceptible-Infected-Removed (SIR) epidemic model and proposes a Generalized SIR (GSIR) model that is an integrative model encompassing multiple waves of daily reported cases. Existing growth function models of epidemic have been shown as the special cases of the GSIR model. Dynamic modeling of the parameters reflect the impact of policy decisions, social awareness, and the availability of medication during the pandemic. GSIR framework can be utilized to find a good fit or predictive model for any pandemic. The study is performed on the COVID-19 data for various countries with detailed results for India, Brazil, United States of America (USA), and World. The peak infection, total expected number of COVID-19 cases and thereof deaths, time-varying reproduction number, and various other parameters are estimated from the available data using the proposed methodology. The proposed GSIR model advances the existing theory and yields promising results for continuous predictive monitoring of COVID-19 pandemic.

Estimation of time-varying reproduction numbers underlying epidemiological processes: A new statistical tool for the COVID-19 pandemic

The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical models may not capture the dynamic transmission and removal processes, governed by virus containment strategies taken at various phases of the epidemic. Moreover, few models account for possible inaccuracies of the reported cases. We propose a Poisson model with time-dependent transmission and removal rates to account for possible random errors in reporting and estimate a time-dependent disease reproduction number, which may reflect the effectiveness of virus control strategies. We apply our method to study the pandemic in several severely impacted countries, and analyze and forecast the evolving spread of the coronavirus. We have developed an interactive web application to facilitate readers' use of our method.

Survival dynamical systems: individual-level survival analysis from population-level epidemic models

In this paper, we show that solutions to ordinary differential equations describing the large-population limits of Markovian stochastic epidemic models can be interpreted as survival or cumulative hazard functions when analysing data on individuals sampled from the population. We refer to the individual-level survival and hazard functions derived from population-level equations as a survival dynamical system (SDS). To illustrate how population-level dynamics imply probability laws for individual-level infection and recovery times that can be used for statistical inference, we show numerical examples based on synthetic data. In these examples, we show that an SDS analysis compares favourably with a complete-data maximum-likelihood analysis. Finally, we use the SDS approach to analyse data from a 2009 influenza A(H1N1) outbreak at Washington State University.

Network-based analysis of a small Ebola outbreak

We present a method for estimating epidemic parameters in network-based stochastic epidemic models when the total number of infections is assumed to be small. We illustrate the method by reanalyzing the data from the 2014 Democratic Republic of the Congo (DRC) Ebola outbreak described in Maganga et al. (2014).

Modelling Ebola

This paper is the combination of a review on the problems of data collection and modelling efforts of the recent Ebola epidemics. After a brief review of data availability, the modelling frameworks have been discussed. Both deterministic and stochastic models have been reviewed and supplemented with a short discussion of some problems of parameter estimation. The methods have been illustrated by a realistic case study. A hint is given for the scope and limits of prediction and control.

From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges

Since their earliest days, humans have been struggling with infectious diseases. Caused by viruses, bacteria, protozoa, or even higher organisms like worms, these diseases depend critically on numerous intricate interactions between parasites and hosts, and while we have learned much about these interactions, many details are still obscure. It is evident that the combined host-parasite dynamics constitutes a complex system that involves components and processes at multiple scales of time, space, and biological organization. At one end of this hierarchy we know of individual molecules that play crucial roles for the survival of a parasite or for the response and survival of its host. At the other end, one realizes that the spread of infectious diseases by far exceeds specific locales and, due to today's easy travel of hosts carrying a multitude of organisms, can quickly reach global proportions. The community of mathematical modelers has been addressing specific aspects of infectious diseases for a long time. Most of these efforts have focused on one or two select scales of a multi-level disease and used quite different computational approaches. This restriction to a molecular, physiological, or epidemiological level was prudent, as it has produced solid pillars of a foundation from which it might eventually be possible to launch comprehensive, multi-scale modeling efforts that make full use of the recent advances in biology and, in particular, the various high-throughput methodologies accompanying the emerging -omics revolution. This special issue contains contributions from biologists and modelers, most of whom presented and discussed their work at the workshop From within Host Dynamics to the Epidemiology of Infectious Disease, which was held at the Mathematical Biosciences Institute at Ohio State University in April 2014. These contributions highlight some of the forays into a deeper understanding of the dynamics between parasites and their hosts, and the consequences of this dynamics for the spread and treatment of infectious diseases.

WITHDRAWN: From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges

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