scholarly journals Critical fluctuations in epidemic models explain COVID-19 post-lockdown dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Maíra Aguiar ◽  
Joseba Bidaurrazaga Van-Dierdonck ◽  
Javier Mar ◽  
Nicole Cusimano ◽  
Damián Knopoff ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Threshold Value ◽  
Critical Value ◽  
Control Measures ◽  
Supercritical Regime ◽  
Reproduction Ratio ◽  
Critical Fluctuations ◽  
Complex Models ◽  
Disease Spreading

AbstractAs the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves, even when the community disease transmission rate $$\beta$$ β is not significantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, $$\beta > \beta _c$$ β > β c ) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, $$\beta < \beta _c$$ β < β c ) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with $$r(t) \approx 1$$ r ( t ) ≈ 1 hovering around its threshold value.

scholarly journals An epidemic model for non-first-order transmission kinetics

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0247512
Author(s):  
Eun-Young Mun ◽  
Feng Geng
Keyword(s):  
Epidemic Model ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Early Stage ◽  
Compartmental Models ◽  
Control Measures ◽  
Chemical Reaction Kinetics ◽  
Rate Law ◽  
First Order ◽  
First Order Kinetics

Compartmental models in epidemiology characterize the spread of an infectious disease by formulating ordinary differential equations to quantify the rate of disease progression through subpopulations defined by the Susceptible-Infectious-Removed (SIR) scheme. The classic rate law central to the SIR compartmental models assumes that the rate of transmission is first order regarding the infectious agent. The current study demonstrates that this assumption does not always hold and provides a theoretical rationale for a more general rate law, inspired by mixed-order chemical reaction kinetics, leading to a modified mathematical model for non-first-order kinetics. Using observed data from 127 countries during the initial phase of the COVID-19 pandemic, we demonstrated that the modified epidemic model is more realistic than the classic, first-order-kinetics based model. We discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n. While k finds utility in evaluating the effectiveness of control measures due to its responsiveness to external factors, n is more closely related to the intrinsic properties of the epidemic agent, including reproductive ability. The rate law for the modified compartmental SIR model is generally applicable to mixed-kinetics disease transmission with heterogeneous transmission mechanisms. By analyzing early-stage epidemic data, this modified epidemic model may be instrumental in providing timely insight into a new epidemic and developing control measures at the beginning of an outbreak.

scholarly journals Transmission of bovine leukaemia virus within dairy herds by simulation modelling

2006 ◽  
Vol 135 (5) ◽  
pp. 722-732 ◽  
Author(s):  
G. E. MONTI ◽  
K. FRANKENA ◽  
M. C. M. De JONG
Keyword(s):  
Transmission Rate ◽  
Control Measures ◽  
Dairy Herds ◽  
Published Data ◽  
Bovine Leukaemia Virus ◽  
Structured Population Model ◽  
Reproduction Ratio ◽  
Leukaemia Virus ◽  
A Minor ◽  
Parameter Values

SUMMARYIn Argentina, bovine leukaemia virus (BLV) infection is common in dairy herds. The country currently has a National Voluntary Control Programme but relatively few farms have enrolled. However, there is increased interest from authorities and farmers to implement regional compulsory programmes but there is scarce quantitative information of the transmission of BLV in cattle herds. This information is a prerequisite to develop effective BLV control strategies. Mathematical modelling offers ways of integrating population-level knowledge and epidemiological data to predict the outcomes of intervention scenarios. The purpose of the current paper is to gain understanding about the dynamics of the transmission of BLV in dairy herds from Argentina by simulation and to compare various BLV transmission models and select the one that is most appropriate. The hypothetical herd is conceptually described in terms of BLV status as a population of individuals that are protected by maternal antibodies (M), that are susceptible (S), that are in the latent period (E) or that are infectious (I). BLV is spread by horizontal and vertical transmission. We used an age-structured population model and within-herd transmission was simulated by Monte Carlo techniques. The next-generation approach has been used for the systematic computation of the basic reproduction ratio (R0). Parameter values for disease transmission were derived from previously published data; rates of entry, exit or transition between age groups were calculated based on our previous study, observational data, expert opinions and literature. With these parameter values the probability of a minor outbreak was estimated to be 10%, the probability of extinction was estimated as <0·001% and the expected time to extinction as more than 80 years. The probability of a minor outbreak and changes in prevalence were different when the index case was an adult cow compared to introduction by a heifer. Prediction of prevalences from MSI models fit the data satisfactorily. R0 was estimated as 9·5. The sensitivity analysis on R0 showed that all measures directed to reduce the transmission rate are potentially effective given operational control measures. An important prediction of these models is that, even in a relatively small, closed dairy herd, the time-scale for a BLV outbreak may be as long as several years and within-herd control of BLV requires intensive efforts.

scholarly journals Modelling COVID 19 in the Basque Country from introduction to control measure response

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Maíra Aguiar ◽  
Eduardo Millán Ortuondo ◽  
Joseba Bidaurrazaga Van-Dierdonck ◽  
Javier Mar ◽  
Nico Stollenwerk
Keyword(s):  
Disease Transmission ◽  
Hospital Admissions ◽  
Task Force ◽  
Control Measure ◽  
Basque Country ◽  
Epidemiological Data ◽  
Control Measures ◽  
Model Framework ◽  
Modeling Framework ◽  
Reproduction Ratio

Abstract In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system’s necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. The growth rate $$ \lambda $$ λ was calculated from the model and from the data and the implications for the reproduction ratio r are shown. The analysis of the growth rates from the data led to improved model versions describing after the exponential phase also the new information obtained during the phase of response to the control measures. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of “social distancing” and home quarantining.

scholarly journals Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Xi Huo ◽  
Jing Chen ◽  
Shigui Ruan
Keyword(s):  
Disease Transmission ◽  
Large Scale ◽  
Transmission Rate ◽  
Control Strategies ◽  
Herd Immunity ◽  
Antibody Prevalence ◽  
Screening Process ◽  
Vaccination Programs ◽  
Prevalence Level ◽  
The Impact

Abstract Background The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. Methods By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. Results We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. Conclusions We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

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 The Global Behavior of a Periodic Epidemic Model with Travel between Patches

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Luosheng Wen ◽  
Bin Long ◽  
Xin Liang ◽  
Fengling Zeng
Keyword(s):  
Epidemic Model ◽  
Transmission Rate ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Periodic Transmission ◽  
Theoretical Results ◽  
Disease Free

We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.

scholarly journals THRESHOLD VALUE OF THREE-DIMENSIONAL BOOTSTRAP PERCOLATION

2003 ◽  
Vol 14 (04) ◽  
pp. 529-536 ◽  
Author(s):  
DIRK KURTSIEFER
Keyword(s):  
Present Article ◽  
Three Dimensional ◽  
Threshold Value ◽  
Critical Value ◽  
Bootstrap Percolation ◽  
Infinite Lattice

The present article deals with the critical value pc of the three-dimensional bootstrap percolation. We will check the behavior of pc for different lengths of the lattice and additionally we will scale pc in the limit of an infinite lattice.

scholarly journals The effects of flooding and weather conditions on leptospirosis transmission in Thailand

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sudarat Chadsuthi ◽  
Karine Chalvet-Monfray ◽  
Anuwat Wiratsudakul ◽  
Charin Modchang
Keyword(s):  
Sensitivity Analysis ◽  
Public Education ◽  
Mathematical Models ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Weather Conditions ◽  
Transmission Dynamics ◽  
Multiplication Rate ◽  
High Degree ◽  
Transmission Models

AbstractThe epidemic of leptospirosis in humans occurs annually in Thailand. In this study, we have developed mathematical models to investigate transmission dynamics between humans, animals, and a contaminated environment. We compared different leptospire transmission models involving flooding and weather conditions, shedding and multiplication rate in a contaminated environment. We found that the model in which the transmission rate depends on both flooding and temperature, best-fits the reported human data on leptospirosis in Thailand. Our results indicate that flooding strongly contributes to disease transmission, where a high degree of flooding leads to a higher number of infected individuals. Sensitivity analysis showed that the transmission rate of leptospires from a contaminated environment was the most important parameter for the total number of human cases. Our results suggest that public education should target people who work in contaminated environments to prevent Leptospira infections.

scholarly journals Mother-child transmission of Chagas disease: could coinfection with human immunodeficiency virus increase the risk?

2009 ◽  
Vol 42 (2) ◽  
pp. 107-109 ◽  
Author(s):  
Pablo Gustavo Scapellato ◽  
Edgardo Gabriel Bottaro ◽  
María Teresa Rodríguez-Brieschke
Keyword(s):  
Human Immunodeficiency Virus ◽  
Trypanosoma Cruzi ◽  
Chagas Disease ◽  
Vertical Transmission ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Buffy Coat ◽  
Child Transmission ◽  
Serological Tests ◽  
Immunodeficiency Virus

A study was conducted on all newborns from mothers with Chagas disease who were attended at Hospital Donación F. Santojanni between January 1, 2001, and August 31, 2007. Each child was investigated for the presence of Trypanosoma cruzi parasitemia through direct examination of blood under the microscope using the buffy coat method on three occasions during the first six months of life. Serological tests were then performed. Ninety-four children born to mothers infected with Trypanosoma cruzi were attended over the study period. Three of these children were born to mothers coinfected with the human immunodeficiency virus. Vertical transmission of Chagas disease was diagnosed in 13 children, in all cases by identifying parasitemia. The overall Chagas disease transmission rate was 13.8% (13/94). It was 100% (3/3) among the children born to mothers with HIV infection and 10.9% (10/91) among children born to mothers without HIV [Difference = 0.89; CI95 = 0.82-0.95; p = 0.0021]. We concluded that coinfection with HIV could increase the risk of vertical transmission of Chagas disease.

scholarly journals Transmission dynamics of lumpy skin disease in Ethiopia

2017 ◽  
Vol 145 (13) ◽  
pp. 2856-2863 ◽  
Author(s):  
W. MOLLA ◽  
K. FRANKENA ◽  
M. C. M. DE JONG
Keyword(s):  
Production System ◽  
Skin Disease ◽  
Transmission Rate ◽  
Severe Disease ◽  
Livestock Production ◽  
Sir Epidemic Model ◽  
Reproduction Ratio ◽  
Lumpy Skin Disease ◽  
Transmission Parameters ◽  
Intensive Production

SUMMARYLumpy skin disease (LSD) is a severe disease of cattle caused by a Capripoxvirus and often caused epidemics in Ethiopia and many other countries. This study was undertaken to quantify the transmission between animals and to estimate the infection reproduction ratio in a predominantly mixed crop–livestock system and in intensive commercial herd types. The transmission parameters were based on a susceptible-infectious-recovered (SIR) epidemic model with environmental transmission and estimated using generalized linear models. The transmission parameters were estimated using a survival rate of infectious virus in the environment equal to 0·325 per day, a value based on the best-fitting statistical model. The transmission rate parameter between animals was 0·072 (95% CI 0·068–0·076) per day in the crop–livestock production system, whereas this transmission rate in intensive production system was 0·076 (95% CI 0·068–0·085) per day. The reproduction ratio (R) of LSD between animals in the crop–livestock production system was 1·07, whereas it was 1·09 between animals in the intensive production system. The calculated R provides a baseline against which various control options can be assessed for efficacy.

Sign in / Sign up

Export Citation Format

Share Document