Does the Contact Rate Matter for Ceramics?

2014 ◽  
pp. 141-146
Author(s):  
Manjima Bhattacharya ◽  
Riya Chakraborty ◽  
Arjun Dey ◽  
Anoop Mukhopadhyay
Keyword(s):  
Contact Rate

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 Stability analysis of a dynamical model of tuberculosis with incomplete treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ihsan Ullah ◽  
Saeed Ahmad ◽  
Qasem Al-Mdallal ◽  
Zareen A. Khan ◽  
Hasib Khan ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Contact Rate ◽  
Asymptotically Stable ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Efficient Treatment ◽  
Effective Contact ◽  
The Impact ◽  
Incomplete Treatment

Abstract A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio $\Re _{0}$ ℜ 0 ; if $\Re _{0}<1$ ℜ 0 < 1 , there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for $\Re _{0}>1$ ℜ 0 > 1 , a unique positive endemic equilibrium exists which is globally asymptotically stable. The global stability of the equilibria is shown via Lyapunov function. It is also obtained that incomplete treatment of TB causes increase in disease infection while efficient treatment results in a reduction in TB. Finally, for the estimated parameters, some numerical simulations are performed to verify the analytical results. These numerical results indicate that decrease in the effective contact rate λ and increase in the treatment rate γ play a significant role in the TB infection control.

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.

The dynamics of a delayed deterministic and stochastic epidemic SIR models with a saturated incidence rate

2018 ◽  
Vol 26 (4) ◽  
pp. 235-245 ◽  
Author(s):  
Modeste N’zi ◽  
Ilimidi Yattara
Keyword(s):  
Stochastic Model ◽  
White Noise ◽  
Incidence Rate ◽  
Deterministic Model ◽  
Contact Rate ◽  
Almost Sure Stability ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Global Positive Solution ◽  
Disease Free

AbstractWe treat a delayed SIR (susceptible, infected, recovered) epidemic model with a saturated incidence rate and its perturbation through the contact rate using a white noise. We start with a deterministic model and then add a perturbation on the contact rate using a white noise to obtain a stochastic model. We prove the existence and uniqueness of the global positive solution for both deterministic and stochastic delayed differential equations. Under suitable conditions on the parameters, we study the global asymptotic stability of the disease-free equilibrium of the deterministic model and the almost sure stability of the disease-free equilibrium of the stochastic model.

scholarly journals A simple criterion to design optimal non-pharmaceutical interventions for mitigating epidemic outbreaks

2021 ◽  
Vol 18 (178) ◽  
Author(s):  
Marco Tulio Angulo ◽  
Fernando Castaños ◽  
Rodrigo Moreno-Morton ◽  
Jorge X. Velasco-Hernández ◽  
Jaime A. Moreno
Keyword(s):  
Disease Transmission ◽  
Reproduction Number ◽  
Contact Rate ◽  
Simple Criterion ◽  
Societal Costs ◽  
Public Events ◽  
Maximum Decrease ◽  
Minimal Reduction ◽  
Theoretical Results ◽  
Pharmaceutical Interventions

For mitigating the COVID-19 pandemic, much emphasis is made on implementing non-pharmaceutical interventions to keep the reproduction number below one. However, using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significant economic and societal costs. Here, we derive a simple and mathematically rigorous criterion for designing optimal transitory non-pharmaceutical interventions for mitigating epidemic outbreaks. We find that reducing the reproduction number below one is sufficient but not necessary. Instead, our criterion prescribes the required reduction in the reproduction number according to the desired maximum of disease prevalence and the maximum decrease of disease transmission that the interventions can achieve. We study the implications of our theoretical results for designing non-pharmaceutical interventions in 16 cities and regions during the COVID-19 pandemic. In particular, we estimate the minimal reduction of each region’s contact rate necessary to control the epidemic optimally. Our results contribute to establishing a rigorous methodology to design optimal non-pharmaceutical intervention policies for mitigating epidemic outbreaks.

scholarly journals Mathematical model and simulations of MERS outbreak: Predictions and implications for control measures

BIOMATH ◽  
2017 ◽  
Vol 5 (2) ◽  
pp. 1612141 ◽  
Author(s):  
Nofe Al-Asuoad ◽  
Libin Rong ◽  
Sadoof Alaswad ◽  
Meir Shillor
Keyword(s):  
Mathematical Model ◽  
Middle East ◽  
Coupled System ◽  
Control Measures ◽  
Nonlinear Ordinary Differential Equations ◽  
Contact Rate ◽  
Isolation Rate ◽  
Model Predictions ◽  
The World ◽  
The City

The Middle East Respiratory Syndrome (MERS) has been identified in 2012 and since then outbreaks have been reported in various localities in the Middle East and in other parts of the world. To help predict the possible dynamics of MERS, as well as ways to contain it, this paper develops a mathematical model for the disease. It has a compartmental structure similar to SARS models and is in the form of a coupled system of nonlinear ordinary differential equations (ODEs). The model predictions are fitted to data from the outbreaks in Riyadh (Saudi Arabia) during 2013-2016. The results reveal that MERS will eventually be contained in the city. However, the containment time and the severity of the outbreaks depend crucially on the contact coefficients and the isolation rate constant. When randomness is added to the model coefficients, the simulations show that the model is sensitive to the scaled contact rate among people and to the isolation rate. The model is analyzed using stability theory for ODEs and indicates that when using only isolation, the endemic steady state is locally stable and attracting. Numerical simulations with parameters estimated from the city of Riyadh illustrate the analytical results and the model behavior, which may have important implications for the disease containment in the city. Indeed, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. The model is general and may be used to analyze outbreaks in other parts of the Middle East and other areas.

scholarly journals Epidemiological impact of SARS-CoV-2 vaccination: mathematical modeling analyses

2020 ◽  
Author(s):  
Monia Makhoul ◽  
Houssein H. Ayoub ◽  
Hiam Chemaitelly ◽  
Shaheen Seedat ◽  
Ghina R Mumtaz ◽  
...  
Keyword(s):  
Decision Making ◽  
Disease Progression ◽  
Vaccine Development ◽  
Severe Disease ◽  
Herd Immunity ◽  
Social Contact ◽  
Population Level ◽  
Contact Rate ◽  
Disease Case ◽  
Vaccine Impact

AbstractBackgroundSeveral SARS-CoV-2 vaccine candidates are currently in the pipeline. This study aims to inform SARS-CoV-2 vaccine development, licensure, decision-making, and implementation by determining key preferred vaccine product characteristics and associated population-level impact.MethodsVaccination impact was assessed at various efficacies using an age-structured mathematical model describing SARS-CoV-2 transmission and disease progression, with application for China.ResultsA prophylactic vaccine with efficacy against acquisition (VES) of ≥70% is needed to eliminate this infection. A vaccine with VES <70% will still have a major impact, and may control the infection if it reduces infectiousness or infection duration among those vaccinated who acquire the infection, or alternatively if supplemented with a moderate social-distancing intervention (<20% reduction in contact rate), or complemented with herd immunity. Vaccination is cost-effective. For a vaccine with VES of 50%, number of vaccinations needed to avert one infection is only 2.4, one severe disease case is 25.5, one critical disease case is 33.2, and one death is 65.1. Gains in effectiveness are achieved by initially prioritizing those ≥60 years. Probability of a major outbreak is virtually zero with a vaccine with VES ≥70%, regardless of number of virus introductions. Yet, an increase in social contact rate among those vaccinated (behavior compensation) can undermine vaccine impact.ConclusionsEven a partially-efficacious vaccine can offer a fundamental solution to control SARS-CoV-2 infection and at high cost-effectiveness. In addition to the primary endpoint on infection acquisition, developers should assess natural history and disease progression outcomes and/or proxy biomarkers, since such secondary endpoints may prove critical in licensure, decision-making, and vaccine impact.

scholarly journals The Easter and Passover Blip in New York City: How exceptions can cause detrimental effects in pandemic times

2020 ◽  
Author(s):  
Maximilian Vierlboeck ◽  
Roshanak R. Nilchiani ◽  
Christine M. Edwards
Keyword(s):  
New York ◽  
New York City ◽  
Infection Rate ◽  
York City ◽  
Contact Rate ◽  
General Observation ◽  
Executive Summary ◽  
Contact Rates ◽  
Long Run ◽  
Close Proximity

Abstract and Executive SummaryWhen it comes to pandemics such as the currently present COVID-19 [1], various issues and problems arise for infrastructures and institutions. Due to possible extreme effects, such as hospitals potentially running out of beds or medical equipment, it is essential to lower the infection rate to create enough space to attend to the affected people and allow enough time for a vaccine to be developed. Unfortunately, this requires that measures put into place are upheld long enough to reduce the infection rate sufficiently.In this paper, we describe research simulating the influences of the contact rate on the spread of the pandemic using New York City as an example (Section IV) and especially already observed effects of contact rate increases during holidays [2-4] (Section V). In multiple simulations scenarios for Passover and Easter holidays, we evaluated 25%, 50%, 75%, and 100% temporary increases in contact rates using a scenario close to the currently reported numbers as reference and contact rates based on bioterrorism research as a “normal” baseline for NYC.The first general finding from the simulations is that singular events of increased visits/contacts amplify each other disproportionately if they are happening in close proximity (time intervals) together. The second general observation was that contact rate spikes leave a permanently increased and devastating infection rate behind, even after the contact rate returns to the reduced one. In case of a temporary sustained increase of contact rate for just three days in a row, the aftermath results in an increase of infection rate up to 40%, which causes double the fatalities in the long run.In numbers, given that increases of 25% and 50% seem to be most likely given the data seen in Germany for the Easter weekend for example [2, 3], our simulations show the following increases (compared to the realistic reference run): for a temporary 25% surge in contact rate, the total cases grew by 215,880, the maximum of required hospitalizations over time increased to 63,063, and the total fatalities climbed by 8,844 accumulated over 90 days. As for the 50% surge, we saw the total number of cases rise by 461,090, the maximum number of required hospitalizations increase to 79,733, and the total number of fatalities climb by 19,125 over 90 days in NYC.All in all, we conclude that even very short, temporary increases in contact rates can have disproportionate effects and result in unrecoverable phenomena that can hardly be reversed or managed later. The numbers show possible phenomena before they might develop effects in reality. This is important because phenomena such as the described blip can impact the hospitals in reality. Therefore, we warn that a wave of infections due to increased contact rates during Passover/Easter might come as a result!

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