scholarly journals Pandemic spread in communities via random graphs

2021 ◽  
Vol 2021 (11) ◽  
pp. 113501
Author(s):  
Dor Minzer ◽  
Yaron Oz ◽  
Muli Safra ◽  
Lior Wainstain
Keyword(s):  
Branching Process ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Connected Component ◽  
Natural Evolution ◽  
Contact Graph ◽  
Process Framework ◽  
The Difference ◽  
Number Of Individuals ◽  
The Basic Reproduction Number

Abstract Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline the contacts between individuals in distinct communities. Given these parameters, we determine whether there will be an outbreak and if yes, we calculate the size of the giant-connected-component of the graph, thereby, determining the fraction of the population of each type that would be infected before it ends. We show that the pandemic spread has a natural evolution direction given by the Perron–Frobenius eigenvector of a matrix whose entries encode the average number of individuals of one type expected to be infected by an individual of another type. The corresponding eigenvalue is the basic reproduction number of the pandemic. We perform numerical simulations that compare homogeneous and heterogeneous spread graphs and quantify the difference between them. We elaborate on the difference between herd immunity and the end of the pandemic and the effect of countermeasures on the fraction of infected population.

scholarly journals Flattening the curve is not enough, we need to squash it: An explainer using a simple model

2020 ◽  
Author(s):  
ES McBryde ◽  
MT Meehan ◽  
JM Trauer
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Herd Immunity ◽  
International Travel ◽  
Effective Control ◽  
Curve Versus ◽  
Successful Control ◽  
The Difference ◽  
The Uk ◽  
Local Transmission

AbstractBackgroundAround the world there are examples of both effective control (e.g., South Korea, Japan) and less successful control (e.g., Italy, Spain, United States) of COVID-19 with dramatic differences in the consequent epidemic curves. Models agree that flattening the curve without controlling the epidemic completely is insufficient and will lead to an overwhelmed health service. A recent model, calibrated for the UK and US, demonstrated this starkly.MethodsWe used a simple compartmental deterministic model of COVID-19 transmission in Australia, to illustrate the dynamics resulting from shifting or flattening the curve versus completely squashing it.ResultsWe find that when the reproduction number is close to one, a small decrease in transmission leads to a large reduction in burden (i.e., cases, deaths and hospitalisations), but achieving this early in the epidemic through social distancing interventions also implies that the community will not reach herd immunity.ConclusionsAustralia needs not just to shift and flatten the curve, but to squash it by getting the reproduction number below one. This will require Australia to achieve transmission rates at least two thirds lower than those seen in the most severely affected countries.The knownCOVID-19 has been diagnosed in over 4,000 Australians. Up until mid-March, most were from international travel, but now we are seeing a rise in locally acquired cases.The newThis study uses a simple transmission dynamic model to demonstrate the difference between moderate changes to the reproduction number and forcing the reproduction number below one.The implicationsLowering local transmission is becoming important in reducing the transmission of COVID-19. To maintain control of the epidemic, the focus should be on those in the community who do not regard themselves as at risk.

scholarly journals The basic reproduction number and herd immunity for COVID-19 in India

2021 ◽  
Vol 14 (35) ◽  
pp. 2773-2777
Author(s):  
Mohit Soni ◽  
◽  
Rajesh Kumar Sharma ◽  
Shivram Sharma
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Herd Immunity ◽  
The Basic Reproduction Number

scholarly journals Variation in natural exposure to anopheles mosquitoes and its effects on malaria transmission

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Wamdaogo M Guelbéogo ◽  
Bronner Pamplona Gonçalves ◽  
Lynn Grignard ◽  
John Bradley ◽  
Samuel S Serme ◽  
...  
Keyword(s):  
Malaria Transmission ◽  
Significant Variation ◽  
Reproduction Number ◽  
Infection Risk ◽  
Transmission Potential ◽  
Anopheles Mosquitoes ◽  
Natural Exposure ◽  
Number Of Individuals ◽  
Blood Meals ◽  
The Basic Reproduction Number

Variation in biting frequency by Anopheles mosquitoes can explain some of the heterogeneity in malaria transmission in endemic areas. In this study in Burkina Faso, we assessed natural exposure to mosquitoes by matching the genotype of blood meals from 1066 mosquitoes with blood from residents of local households. We observed that the distribution of mosquito bites exceeded the Pareto rule (20/80) in two of the three surveys performed (20/85, 76, and 96) and, at its most pronounced, is estimated to have profound epidemiological consequences, inflating the basic reproduction number of malaria by 8-fold. The distribution of bites from sporozoite-positive mosquitoes followed a similar pattern, with a small number of individuals within households receiving multiple potentially infectious bites over the period of a few days. Together, our findings indicate that heterogeneity in mosquito exposure contributes considerably to heterogeneity in infection risk and suggest significant variation in malaria transmission potential.

scholarly journals Multi-Type Branching Processes Modeling of Nosocomial Epidemics

2017 ◽  
Vol 32 (2) ◽  
Author(s):  
Zeinab Mohamed ◽  
Tamer Oraby
Keyword(s):  
Health Care ◽  
Basic Reproduction Number ◽  
Branching Process ◽  
Negative Binomial ◽  
Reproduction Number ◽  
Branching Processes ◽  
Care Facility ◽  
Health Care Facility ◽  
Different Types ◽  
The Basic Reproduction Number

AbstractNosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number

scholarly journals The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level

2020 ◽  
Author(s):  
Tom Britton ◽  
Frank Ball ◽  
Pieter Trapman
Keyword(s):  
Preventive Measures ◽  
Reproduction Number ◽  
Social Activity ◽  
Herd Immunity ◽  
Contact Rates ◽  
Mixing Rates ◽  
Disease Spreading ◽  
Age Structured ◽  
Induced Immunity ◽  
The Basic Reproduction Number

AbstractMost countries are suffering severely from the ongoing covid-19 pandemic despite various levels of preventive measures. A common question is if and when a country or region will reach herd immunity h. The classical herd immunity level hC is defined as hC = 1−1/R0, where R0 is the basic reproduction number, for covid-19 estimated to lie somewhere in the range 2.2-3.5 depending on country and region. It is shown here that the disease-induced herd immunity level hD, after an outbreak has taken place in a country/region with a set of preventive measures put in place, is actually substantially smaller than hC. As an illustration we show that if R0 = 2.5 in an age-structured community with mixing rates fitted to social activity studies, and also categorizing individuals into three categories: low active, average active and high active, and where preventive measures affect all mixing rates proportionally, then the disease-induced herd immunity level is hD = 43% rather than hC = 1−1/2.5 = 60%. Consequently, a lower fraction infected is required for herd immunity to appear. The underlying reason is that when immunity is induced by disease spreading, the proportion infected in groups with high contact rates is greater than that in groups with low contact rates. Consequently, disease-induced immunity is stronger than when immunity is uniformly distributed in the community as in the classical herd immunity level.

scholarly journals Estimation of measles vaccine efficacy and critical vaccination coverage in a highly vaccinated population

2010 ◽  
Vol 7 (52) ◽  
pp. 1537-1544 ◽  
Author(s):  
Michiel van Boven ◽  
Mirjam Kretzschmar ◽  
Jacco Wallinga ◽  
Philip D O'Neill ◽  
Ole Wichmann ◽  
...  
Keyword(s):  
Public School ◽  
Vaccination Coverage ◽  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Credible Interval ◽  
Final Size ◽  
Measles Elimination ◽  
The Basic Reproduction Number

Measles is a highly infectious disease that has been targeted for elimination from four WHO regions. Whether and under which conditions this goal is feasible is, however, uncertain since outbreaks have been documented in populations with high vaccination coverage (more than 90%). Here, we use the example of a large outbreak in a German public school to show how estimates of key epidemiological parameters such as the basic reproduction number ( R 0 ), vaccine efficacy (VE S ) and critical vaccination coverage ( p c ) can be obtained from partially observed outbreaks in highly vaccinated populations. Our analyses rely on Bayesian methods of inference based on the final size distribution of outbreak size, and use data which are easily collected. For the German public school the analyses indicate that the basic reproduction number of measles is higher than previously thought ( , 95% credible interval: 23.6–40.4), that the vaccine is highly effective in preventing infection ( , 95% credible interval: 0.993–0.999), and that a vaccination coverage in excess of 95 per cent may be necessary to achieve herd immunity ( , 95% credible interval: 0.961–0.978). We discuss the implications for measles elimination from highly vaccinated populations.

scholarly journals Reassessment of contact restrictions and testing campaigns against COVID-19 via spatio-temporal modeling

2021 ◽  
Author(s):  
Naleen Chaminda Ganegoda ◽  
Karunia Putra Wijaya ◽  
Joseph Páez Chávez ◽  
Dipo Aldila ◽  
K. K. W. Hasitha Erandi ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Time Window ◽  
Herd Immunity ◽  
Degree Theory ◽  
Path Following ◽  
Transient Behavior ◽  
Fixed Time ◽  
Mathematical Framework ◽  
The Basic Reproduction Number

AbstractSince the earliest outbreak of COVID-19, the disease continues to obstruct life normalcy in many parts of the world. The present work proposes a mathematical framework to improve non-pharmaceutical interventions during the new normal before vaccination settles herd immunity. The considered approach is built from the viewpoint of decision makers in developing countries where resources to tackle the disease from both a medical and an economic perspective are scarce. Spatial auto-correlation analysis via global Moran’s index and Moran’s scatter is presented to help modulate decisions on hierarchical-based priority for healthcare capacity and interventions (including possible vaccination), finding a route for the corresponding deployment as well as landmarks for appropriate border controls. These clustering tools are applied to sample data from Sri Lanka to classify the 26 Regional Director of Health Services (RDHS) divisions into four clusters by introducing convenient classification criteria. A metapopulation model is then used to evaluate the intra- and inter-cluster contact restrictions as well as testing campaigns under the absence of confounding factors. Furthermore, we investigate the role of the basic reproduction number to determine the long-term trend of the regressing solution around disease-free and endemic equilibria. This includes an analytical bifurcation study around the basic reproduction number using Brouwer Degree Theory and asymptotic expansions as well as related numerical investigations based on path-following techniques. We also introduce the notion of average policy effect to assess the effectivity of contact restrictions and testing campaigns based on the proposed model’s transient behavior within a fixed time window of interest.

scholarly journals Vaccination in a two-group epidemic model

2021 ◽  
Author(s):  
Sebastian Aniţa ◽  
Malay Banerjee ◽  
Samiran Ghosh ◽  
Vitaly Volpert
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Vaccination Campaign ◽  
Vaccination Strategies ◽  
The Difference ◽  
The Basic Reproduction Number

AbstractEpidemic progression depends on the structure of the population. We study a two-group epidemic model with the difference between the groups determined by the rate of disease transmission. The basic reproduction number, the maximal and the total number of infected individuals are characterized by the proportion between the groups. We consider different vaccination strategies and determine the outcome of the vaccination campaign depending on the distribution of vaccinated individuals between the groups.

Stability Analysis of an SEIR Epidemic Model with Stochastic Perturbation and Numerical Simulation

2013 ◽  
Vol 14 (2) ◽  
Author(s):  
Xiaoming Fan ◽  
Zhigang Wang
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Behavior ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Random Fluctuation ◽  
Deterministic System ◽  
Stochastic Version ◽  
Special Case ◽  
The Basic Reproduction Number

AbstractAn SEIR epidemic model with constant immigration and random fluctuation around the endemic equilibrium is considered. As a special case, a deterministic system discussed by Li et al. will be incorporated into the stochastic version given by us. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the basic reproduction number ℛ

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