scholarly journals Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

2020 ◽  
Author(s):  
Marek Kochańczyk ◽  
Frederic Grabowski ◽  
Tomasz Lipniacki
Keyword(s):  
Reproduction Number ◽  
Exponential Phase ◽  
Time Dependent ◽  
Therapeutic Interventions ◽  
Contact Rate ◽  
Epidemic Spread ◽  
Early Exponential Phase ◽  
Contact Rates ◽  
Multiplication Coefficient

We constructed a simple Susceptible–Infected–Infectious–Excluded model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, rC, and exclusion rate, rE. The rates can be manipulated by non-therapeutic interventions and determine the basic reproduction number, R = rC/rE, and, together with τ, the daily multiplication coefficient at the early exponential phase, β. Initial β determines the reduction of rC required to contain epidemic spread. In the long-term, we consider a scenario based on typical social behaviours, in which rC first decreases in response to a surge of daily new cases, forcing people to self-isolate, and then slowly increases when people gradually accept higher risk. Consequently, initial abrupt epidemic spread is followed by a plateau and slow regression. This scenario, although economically and socially devastating, will grant time to develop, produce, and distribute a vaccine, or at least limit daily cases to a manageable number.

scholarly journals Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

2020 ◽  
Vol 15 ◽  
pp. 28 ◽  
Author(s):  
Marek Kochańczyk ◽  
Frederic Grabowski ◽  
Tomasz Lipniacki
Keyword(s):  
Incubation Period ◽  
Reproduction Number ◽  
Exponential Phase ◽  
Contact Rate ◽  
Epidemic Spread ◽  
Early Exponential Phase ◽  
Contact Rates ◽  
Serial Interval ◽  
Hypothetical Scenario ◽  
Multiplication Coefficient

We constructed a simple Susceptible−Exposed–Infectious–Removed model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, β, and exclusion rate, γ. The rates depend on nontherapeutic interventions and determine the basic reproduction number, R0 = β/γ, and, together with τ, the daily multiplication coefficient in the early exponential phase, θ. Initial R0 determines the reduction of β required to contain the spread of the epidemic. We demonstrate that introduction of a cascade of multiple exposed states enables the model to reproduce the distributions of the incubation period and the serial interval reported by epidemiologists. Using the model, we consider a hypothetical scenario in which β is modulated solely by anticipated changes of social behaviours: first, β decreases in response to a surge of daily new cases, pressuring people to self-isolate, and then, over longer time scale, β increases as people gradually accept the risk. In this scenario, initial abrupt epidemic spread is followed by a plateau and slow regression, which, although economically and socially devastating, grants time to develop and deploy vaccine or at least limit daily cases to a manageable number.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Co-circulation of SARS-CoV-2 and Influenza under vaccination scenarios

2021 ◽  
Author(s):  
Manuel A. Acuña-Zegarra ◽  
Mayra Núñez-López ◽  
Andreu Comas-García ◽  
Mario Santana-Cibrian ◽  
Jorge X. Velasco-Hernández
Keyword(s):  
Reproduction Number ◽  
Population Level ◽  
Host Population ◽  
Effective Coverage ◽  
Factors Affecting ◽  
Contact Rates ◽  
Effective Contact ◽  
The One ◽  
Transmission Factors

AbstractThe interaction and possibly interference between viruses infecting a common host population is the problem addressed in this work. We model two viral diseases both of the SIRS type that have similar mechanism of transmission and for which a vaccine exists. The vaccine is characterized by its coverage, induced temporal immunity and efficacy. The population dynamics of both diseases considers infected individuals of each disease and hosts that are susceptible to one but have recovered from the other. We do not incorporate coinfection. We postulate two main transmission factors affecting the effective contact rates: i) that the virus with higher reproduction number can superinfect the one with lower reproduction number and ii) that there is some protection induced by vaccination against the weaker virus that reduces the probability of infection by the stronger virus. Our results indicate that coexistence of the viruses is possible in the long term. The time-dependent effective contact rate may induce either alternating outbreaks of each disease or synchronous outbreaks. We also found the existence of bi-stability triggered by a backward bifurcation, conducive to scenarios where, at the population level, vaccine application may promote persistence of both diseases provided the effective coverage and vaccine efficacy are low.

scholarly journals COVID-19 epidemic scenarios into 2021 based on observed key superdispersion events

2021 ◽  
Author(s):  
Mario Santana-Cibrian ◽  
M. Adrian Acuña-Zegarra ◽  
Carlos E. Rodríguez Hernández-Vela ◽  
Jorge X. Velasco-Hernandez ◽  
Ramsés H. Mena
Keyword(s):  
Time Scale ◽  
Reproduction Number ◽  
Social Activity ◽  
Time Dependent ◽  
Contact Rate ◽  
Main Assumption ◽  
Effective Contact ◽  
Incidence And Mortality ◽  
The Status ◽  
Calendar Dates

Key high transmission dates for the year 2020 are used to create scenarios to model the evolution of the COVID-19 pandemic in several states of Mexico for 2021. These scenarios are obtained through the estimation of a time-dependent contact rate, where the main assumption is that the dynamic of the disease is heavily determined by the mobility and social activity of the population during holidays and other important calendar dates. First, changes in the effective contact rate on predetermined dates of 2020 are estimated. Then, using the instantaneous reproduction number to characterize the status of the epidemic (Rt ≈ 1, Rt > 1 or Rt < 1), this information is used to propose different scenarios for the number of cases and deaths for 2021. The main assumption is that the effective contact rate during 2021 will maintain a similar trend to that observed during 2020 on key calendar dates. All other conditions are assumed to remain constant in the time scale of the projections. The objective is to generate a range of scenarios that could be useful to evaluate the possible evolution of the epidemic and its likely impact on incidence and mortality.

scholarly journals A data first approach to modelling Covid-19

2020 ◽  
Author(s):  
Jayanti Prasad
Keyword(s):  
Reproduction Number ◽  
Model Fitting ◽  
Time Dependent ◽  
Primary Data ◽  
Contact Rate ◽  
Multiple Sources ◽  
Transmission Coefficients ◽  
Varying Coefficients ◽  
Step Procedure ◽  
Time Varying Coefficients

AbstractThe primary data for Covid-19 pandemic is in the form of time series for the number of confirmed, recovered and dead cases. This data is updated every day and is available for most countries from multiple sources such as [Gar20b, iD20]. In this work we present a two step procedure for model fitting to Covid-19 data. In the first step, time dependent transmission coefficients are constructed directly from the data and, in the second step, measures of those (minimum, maximum, mean, median etc.,) are used to set priors for fitting models to data. We call this approach a “data driven approach” or “data first approach”. This scheme is complementary to Bayesian approach and can be used with or without that for parameter estimation. We use the procedure to fit a set of SIR and SIRD models, with time dependent contact rate, to Covid-19 data for a set of most affected countries. We find that SIR and SIRD models with constant transmission coefficients cannot fit Covid-19 data for most countries (mainly because social distancing, lockdown etc., make those time dependent). We find that any time dependent contact rate decaying with time can help to fit SIR and SIRD models for most of the countries. We also present constraints on transmission coefficients and basic reproduction number , as well as effective reproduction number . The main contributions of our work are as follows. (1) presenting a two step procedure for model fitting to Covid-19 data (2) constraining transmission coefficients as well as and , for a set of countries and (3) releasing a python package PyCov19 [Pra20b] that can used to fit a class of compartmental models, with time varying coefficients, to Covid-19 data.

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

2020 ◽  
Author(s):  
Eduardo Atem De Carvalho ◽  
Rogerio Atem De Carvalho
Keyword(s):  
New York ◽  
Reproduction Number ◽  
Moving Average ◽  
Real Data ◽  
Time Dependent ◽  
Initial Value ◽  
Health Authorities ◽  
Reproduction Numbers ◽  
Effect Estimation ◽  
The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

In Situ Tests on Creep Behavior of Rock Mass with Joint or Shearing Zone in Foundation of Large-Scale Hydroelectric Projects

2004 ◽  
Vol 261-263 ◽  
pp. 1097-1102 ◽  
Author(s):  
Jian Liu ◽  
Xia Ting Feng ◽  
Xiu Li Ding ◽  
Huo Ming Zhou
Keyword(s):  
Rock Mass ◽  
Creep Behavior ◽  
Large Scale ◽  
Time Dependent ◽  
Three Gorges Project ◽  
Three Gorges ◽  
The Three Gorges ◽  
The Three Gorges Project

The time-dependent behavior of rock mass, which is generally governed by joints and shearing zones, is of great significance for engineering design and prediction of long-term deformation and stability. In situ creep test is a more effective method than laboratory test in characterizing the creep behavior of rock mass with joint or shearing zone due to the complexity of field conditions. A series of in situ creep tests on granite with joint at the shiplock area of the Three-Gorges Project and basalt with shearing zone at the right abutment of the Xiluodu Project were performed in this study. Based on the test results, the stress-displacement-time responses of the joints and basalt are analyzed, and their time-dependent constitutive model and model coefficients are given, which is crucial for the design to prevent the creep deformations of rock masses from causing the failure of the operation of the shiplock gate at the Three-Gorges Project and long-term stability of the Xiluodu arc dam.

scholarly journals A cross-sectional study measuring contact patterns using diaries in an urban and a rural community in South Africa, 2018

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Jackie Kleynhans ◽  
Stefano Tempia ◽  
Meredith L. McMorrow ◽  
Anne von Gottberg ◽  
Neil A. Martinson ◽  
...  
Keyword(s):  
South Africa ◽  
Age Groups ◽  
Cross Sectional Study ◽  
Rural Site ◽  
Urban Site ◽  
Contact Rate ◽  
Sectional Study ◽  
Cross Sectional ◽  
Contact Rates ◽  
Contact Patterns

Abstract Background Describing contact patterns is crucial to understanding infectious disease transmission dynamics and guiding targeted transmission mitigation interventions. Data on contact patterns in Africa, especially South Africa, are limited. We measured and compared contact patterns in a rural and urban community, South Africa. We assessed participant and contact characteristics associated with differences in contact rates. Methods We conducted a cross-sectional study nested in a prospective household cohort study. We interviewed participants to collect information on persons in contact with for one day. We described self-reported contact rates as median number people contacted per day, assessed differences in contact rates based on participant characteristics using quantile regression, and used a Poisson model to assess differences in contact rates based on contact characteristics within age groups. We also calculated cumulative person hours in contact within age groups at different locations. Results We conducted 535 interviews (269 rural, 266 urban), with 17,252 contacts reported. The overall contact rate was 14 (interquartile range (IQR) 9–33) contacts per day. Those ≤18 years had higher contact rates at the rural site (coefficient 17, 95% confidence interval (95%CI) 10–23) compared to the urban site, for those aged 14–18 years (13, 95%CI 3–23) compared to < 7 years. No differences were observed for adults. There was a strong age-based mixing, with age groups interacting more with similar age groups, but also interaction of participants of all ages with adults. Children aged 14–18 years had the highest cumulative person hours in contact (116.3 rural and 76.4 urban). Conclusions Age played an important role in the number and duration of contact events, with children at the rural site having almost double the contact rate compared to the urban site. These contact rates can be utilized in mathematical models to assess transmission dynamics of infectious diseases in similar communities.

scholarly journals The challenges of containing SARS-CoV-2 via test-trace-and-isolate

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sebastian Contreras ◽  
Jonas Dehning ◽  
Matthias Loidolt ◽  
Johannes Zierenberg ◽  
F. Paul Spitzner ◽  
...  
Keyword(s):  
Analytical Model ◽  
Reproduction Number ◽  
Tipping Points ◽  
Social Distancing ◽  
Promising Tool

AbstractWithout a cure, vaccine, or proven long-term immunity against SARS-CoV-2, test-trace-and-isolate (TTI) strategies present a promising tool to contain its spread. For any TTI strategy, however, mitigation is challenged by pre- and asymptomatic transmission, TTI-avoiders, and undetected spreaders, which strongly contribute to ”hidden" infection chains. Here, we study a semi-analytical model and identify two tipping points between controlled and uncontrolled spread: (1) the behavior-driven reproduction number $${R}_{t}^{H}$$ R t H of the hidden chains becomes too large to be compensated by the TTI capabilities, and (2) the number of new infections exceeds the tracing capacity. Both trigger a self-accelerating spread. We investigate how these tipping points depend on challenges like limited cooperation, missing contacts, and imperfect isolation. Our results suggest that TTI alone is insufficient to contain an otherwise unhindered spread of SARS-CoV-2, implying that complementary measures like social distancing and improved hygiene remain necessary.

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