scholarly journals Infectious disease control using contact tracing in random and scale-free networks

2005 ◽  
Vol 3 (6) ◽  
pp. 55-62 ◽  
Author(s):  
Istvan Z Kiss ◽  
Darren M Green ◽  
Rowland R Kao
Keyword(s):  
Transmission Rate ◽  
Removal Rate ◽  
Latency Period ◽  
Average Degree ◽  
Contact Tracing ◽  
Random Networks ◽  
Scale Free ◽  
Epidemic Size ◽  
Advanced Stages ◽  
Final Epidemic Size

Contact tracing aims to identify and isolate individuals that have been in contact with infectious individuals. The efficacy of contact tracing and the hierarchy of traced nodes—nodes with higher degree traced first—is investigated and compared on random and scale-free (SF) networks with the same number of nodes N and average connection K . For values of the transmission rate larger than a threshold, the final epidemic size on SF networks is smaller than that on corresponding random networks. While in random networks new infectious and traced nodes from all classes have similar average degrees, in SF networks the average degree of nodes that are in more advanced stages of the disease is higher at any given time. On SF networks tracing removes possible sources of infection with high average degree. However a higher tracing effort is required to control the epidemic than on corresponding random networks due to the high initial velocity of spread towards the highly connected nodes. An increased latency period fails to significantly improve contact tracing efficacy. Contact tracing has a limited effect if the removal rate of susceptible nodes is relatively high, due to the fast local depletion of susceptible nodes.

EXACT ANALYTICAL EXPRESSIONS FOR THE FINAL EPIDEMIC SIZE OF AN SIR MODEL ON SMALL NETWORKS

2016 ◽  
Vol 57 (4) ◽  
pp. 429-444 ◽  
Author(s):  
K. MCCULLOCH ◽  
M. G. ROBERTS ◽  
C. R. LAING
Keyword(s):  
Initial Conditions ◽  
Transmission Rate ◽  
Sir Model ◽  
Contact Network ◽  
Sir Epidemic Model ◽  
Node Number ◽  
Sir Epidemic ◽  
Epidemic Size ◽  
Final Epidemic Size ◽  
Analytical Expressions

We investigate the dynamics of a susceptible infected recovered (SIR) epidemic model on small networks with different topologies, as a stepping stone to determining how the structure of a contact network impacts the transmission of infection through a population. For an SIR model on a network of$N$nodes, there are$3^{N}$configurations that the network can be in. To simplify the analysis, we group the states together based on the number of nodes in each infection state and the symmetries of the network. We derive analytical expressions for the final epidemic size of an SIR model on small networks composed of three or four nodes with different topological structures. Differential equations which describe the transition of the network between states are also derived and solved numerically to confirm our analysis. A stochastic SIR model is numerically simulated on each of the small networks with the same initial conditions and infection parameters to confirm our results independently. We show that the structure of the network, degree of the initial infectious node, number of initial infectious nodes and the transmission rate all significantly impact the final epidemic size of an SIR model on small networks.

Edge-based SEIR dynamics with recovery rate in latent period on complex networks

2020 ◽  
Vol 31 (04) ◽  
pp. 2050057
Author(s):  
Rong Zhou ◽  
Qingchu Wu
Keyword(s):  
Latent Period ◽  
Recovery Rate ◽  
Stochastic Simulations ◽  
Epidemic Threshold ◽  
Seir Model ◽  
Scale Free ◽  
Epidemic Size ◽  
Final Epidemic Size ◽  
Full Analysis ◽  
Edge Based

Disease and information spreading on social and information networks have often been described by ordinary differential equations. A recent research by the authors [Y. Wang et al., Commun. Nonlinear Sci. Numer. Simulat. 45, 35 (2017).] presented an analysis of susceptible-exposed-infected-recovered (SEIR) model with and without infectious force in latent period. We present a full analysis in the more general scenario where the exposed nodes can get vaccinated or recovered. The basic reproduction number and the final epidemic size are theoretically derived. Compared to the standard SEIR model without recovery rate in latent period, our results reveal that both the recovery rate in latent period and the length of latent period can increase the epidemic threshold and inhibit the epidemic outbreak. In addition, the model predictions agree well with the continuous-time stochastic simulations in Erdős–Rényi random graphs and scale-free configuration networks.

scholarly journals Disease contact tracing in random and clustered networks

2005 ◽  
Vol 272 (1570) ◽  
pp. 1407-1414 ◽  
Author(s):  
Istvan Z Kiss ◽  
Darren M Green ◽  
Rowland R Kao
Keyword(s):  
Disease Transmission ◽  
Latency Period ◽  
Foot And Mouth Disease ◽  
Stochastic Simulations ◽  
Moment Closure ◽  
Contact Tracing ◽  
Dominant Factor ◽  
Epidemic Size ◽  
Precise Knowledge ◽  
Models Of Disease

The efficacy of contact tracing, be it between individuals (e.g. sexually transmitted diseases or severe acute respiratory syndrome) or between groups of individuals (e.g. foot-and-mouth disease; FMD), is difficult to evaluate without precise knowledge of the underlying contact structure; i.e. who is connected to whom? Motivated by the 2001 FMD epidemic in the UK, we determine, using stochastic simulations and deterministic ‘moment closure’ models of disease transmission on networks of premises (nodes), network and disease properties that are important for contact tracing efficiency. For random networks with a high average number of connections per node, little clustering of connections and short latency periods, contact tracing is typically ineffective. In this case, isolation of infected nodes is the dominant factor in determining disease epidemic size and duration. If the latency period is longer and the average number of connections per node small, or if the network is spatially clustered, then the contact tracing performs better and an overall reduction in the proportion of nodes that are removed during an epidemic is observed.

scholarly journals Impact of public health interventions to curb SARS-CoV-2 spread assessed by an evidence-educated Delphi panel and tailored SEIR model

2021 ◽  
Author(s):  
Bernd Brüggenjürgen ◽  
Hans-Peter Stricker ◽  
Lilian Krist ◽  
Miriam Ortiz ◽  
Thomas Reinhold ◽  
...  
Keyword(s):  
Public Health ◽  
Transmission Rate ◽  
Latency Period ◽  
Policy Decision ◽  
Sensitivity Analyses ◽  
Delphi Panel ◽  
Time Step ◽  
Seir Model ◽  
Health Policy Decision ◽  
The Impact

Abstract Aim To use a Delphi-panel-based assessment of the effectiveness of different non-pharmaceutical interventions (NPI) in order to retrospectively approximate and to prospectively predict the SARS-CoV-2 pandemic progression via a SEIR model (susceptible, exposed, infectious, removed). Methods We applied an evidence-educated Delphi-panel approach to elicit the impact of NPIs on the SARS-CoV-2 transmission rate R0 in Germany. Effectiveness was defined as the product of efficacy and compliance. A discrete, deterministic SEIR model with time step of 1 day, a latency period of 1.8 days, duration of infectiousness of 5 days, and a share of the total population of 15% assumed to be protected by immunity was developed in order to estimate the impact of selected NPI measures on the course of the pandemic. The model was populated with the Delphi-panel results and varied in sensitivity analyses. Results Efficacy and compliance estimates for the three most effective NPIs were as follows: test and isolate 49% (efficacy)/78% (compliance), keeping distance 42%/74%, personal protection masks (cloth masks or other face masks) 33%/79%. Applying all NPI effectiveness estimates to the SEIR model resulted in a valid replication of reported occurrence of the German SARS-CoV-2 pandemic. A combination of four NPIs at consented compliance rates might curb the CoViD-19 pandemic. Conclusion Employing an evidence-educated Delphi-panel approach can support SARS-CoV-2 modelling. Future curbing scenarios require a combination of NPIs. A Delphi-panel-based NPI assessment and modelling might support public health policy decision making by informing sequence and number of needed public health measures.

Heterogeneity in epidemic models and its effect on the spread of infection

1998 ◽  
Vol 35 (3) ◽  
pp. 651-661 ◽  
Author(s):  
Håkan Andersson ◽  
Tom Britton
Keyword(s):  
Heterogeneous Population ◽  
Epidemic Models ◽  
Homogeneous Population ◽  
Epidemic Size ◽  
Infection Pressure ◽  
Group A ◽  
Final Epidemic Size ◽  
Spread Of Infection ◽  
Very High ◽  
High Infectivity

We first study an epidemic amongst a population consisting of individuals with the same infectivity but with varying susceptibilities to the disease. The asymptotic final epidemic size is compared with the corresponding size for a homogeneous population. Then we group a heterogeneous population into households, assuming very high infectivity within households, and investigate how the global infection pressure is affected by rearranging individuals between the households. In both situations considered, it turns out that whether or not homogenizing the individuals or households will result in an increased spread of infection actually depends on the infectiousness of the disease.

scholarly journals Modeling the impact of school reopening and contact tracing strategies on Covid-19 dynamics in different epidemiologic settings in Brazil

2021 ◽  
Author(s):  
Marcelo Eduardo Borges ◽  
Leonardo Souto Ferreira ◽  
Silas Poloni ◽  
Ângela Maria Bagattini ◽  
Caroline Franco ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Disease Incidence ◽  
Demographic Data ◽  
School Closure ◽  
Mitigation Measures ◽  
Contact Tracing ◽  
School Closures ◽  
Infection Transmission ◽  
The Impact

Among the various non–pharmaceutical interventions implemented in response to the Covid–19 pandemic during 2020, school closures have been in place in several countries to reduce infection transmission. Nonetheless, the significant short and long–term impacts of prolonged suspension of in–person classes is a major concern. There is still considerable debate around the best timing for school closure and reopening, its impact on the dynamics of disease transmission, and its effectiveness when considered in association with other mitigation measures. Despite the erratic implementation of mitigation measures in Brazil, school closures were among the first measures taken early in the pandemic in most of the 27 states in the country. Further, Brazil delayed the reopening of schools and stands among the countries in which schools remained closed for the most prolonged period in 2020. To assess the impact of school reopening and the effect of contact tracing strategies in rates of Covid–19 cases and deaths, we model the epidemiological dynamics of disease transmission in 3 large urban centers in Brazil under different epidemiological contexts. We implement an extended SEIR model stratified by age and considering contact networks in different settings – school, home, work, and elsewhere, in which the infection transmission rate is affected by various intervention measures. After fitting epidemiological and demographic data, we simulate scenarios with increasing school transmission due to school reopening. Our model shows that reopening schools results in a non–linear increase of reported Covid-19 cases and deaths, which is highly dependent on infection and disease incidence at the time of reopening. While low rates of within[&ndash]school transmission resulted in small effects on disease incidence (cases/100,000 pop), intermediate or high rates can severely impact disease trends resulting in escalating rates of new cases even if other interventions remain unchanged. When contact tracing and quarantining are restricted to school and home settings, a large number of daily tests is required to produce significant effects of reducing the total number of hospitalizations and deaths. Our results suggest that policymakers should carefully consider the epidemiological context and timing regarding the implementation of school closure and return of in-person school activities. Also, although contact tracing strategies are essential to prevent new infections and outbreaks within school environments, our data suggest that they are alone not sufficient to avoid significant impacts on community transmission in the context of school reopening in settings with high and sustained transmission rates.

scholarly journals Asymptomatic individuals can increase the final epidemic size under adaptive human behavior

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Baltazar Espinoza ◽  
Madhav Marathe ◽  
Samarth Swarup ◽  
Mugdha Thakur
Keyword(s):  
Planning Horizon ◽  
Infection Risk ◽  
Epidemiological Models ◽  
Epidemic Size ◽  
Behavioral Adaptations ◽  
Future State ◽  
Final Epidemic Size ◽  
Asymptomatic Individuals ◽  
The Impact ◽  
Finite Planning Horizon

AbstractInfections produced by non-symptomatic (pre-symptomatic and asymptomatic) individuals have been identified as major drivers of COVID-19 transmission. Non-symptomatic individuals, unaware of the infection risk they pose to others, may perceive themselves—and be perceived by others—as not presenting a risk of infection. Yet, many epidemiological models currently in use do not include a behavioral component, and do not address the potential consequences of risk misperception. To study the impact of behavioral adaptations to the perceived infection risk, we use a mathematical model that incorporates the behavioral decisions of individuals, based on a projection of the system’s future state over a finite planning horizon. We found that individuals’ risk misperception in the presence of non-symptomatic individuals may increase or reduce the final epidemic size. Moreover, under behavioral response the impact of non-symptomatic infections is modulated by symptomatic individuals’ behavior. Finally, we found that there is an optimal planning horizon that minimizes the final epidemic size.

Diffusion/Contagion Processes on Social Networks

2020 ◽  
Vol 47 (2) ◽  
pp. 235-248 ◽  
Author(s):  
Thomas W. Valente ◽  
George G. Vega Yon
Keyword(s):  
Diffusion Of Innovations ◽  
Small World ◽  
Opinion Leadership ◽  
Random Networks ◽  
Degree Centrality ◽  
Health Educators ◽  
Normal Threshold ◽  
Scale Free ◽  
Threshold Distribution ◽  
New Ideas

This study models how new ideas, practices, or diseases spread within and between communities, the diffusion of innovations or contagion. Several factors affect diffusion such as the characteristics of the initial adopters, the seeds; the structure of the network over which diffusion occurs; and the shape of the threshold distribution, which is the proportion of prior adopting peers needed for the focal individual to adopt. In this study, seven seeding conditions are modeled: (1) three opinion leadership indicators, (2) two bridging measures, (3) marginally positioned seeds, and (4) randomly selected seeds for comparison. Three network structures are modeled: (1) random, (2) small-world, and (3) scale-free. Four threshold distributions are modeled: (1) normal; (2) uniform; (3) beta 7,14; and (4) beta 1,2; all of which have a mean threshold of 33%, with different variances. The results show that seeding with nodes high on in-degree centrality and/or inverse constraint has faster and more widespread diffusion. Random networks had faster and higher prevalence of diffusion than scale-free ones, but not different from small-world ones. Compared with the normal threshold distribution, the uniform one had faster diffusion and the beta 7,14 distribution had slower diffusion. Most significantly, the threshold distribution standard deviation was associated with rate and prevalence such that higher threshold standard deviations accelerated diffusion and increased prevalence. These results underscore factors that health educators and public health advocates should consider when developing interventions or trying to understand the potential for behavior change.

scholarly journals Network topology optimization by turning non-scale-free networks into scale-free networks using nonlinear preferential rewiring method

2018 ◽  
Vol 14 (11) ◽  
pp. 155014771878447 ◽  
Author(s):  
Feng Su ◽  
Peijiang Yuan ◽  
Yuanwei Liu ◽  
Shuangqian Cao
Keyword(s):  
Topology Optimization ◽  
Network Topology ◽  
Random Networks ◽  
Practical Application ◽  
Performance Simulation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Network Topologies ◽  
Network Topology Optimization ◽  
Rigorous Mathematical Model

In practical application, the generation and evolution of many real networks always do not follow rigorous mathematical model, making network topology optimization a great challenge in the field of complex networks. In this research, we optimize the topology of non-scale-free networks by turning it into scale-free networks using a nonlinear preferential rewiring method. For different kinds of original networks generated by Watts and Strogatz model, we systematically demonstrate the optimization process and the modified networks to verify the performance of nonlinear preferential rewiring. We conduct further researches to explore the effect of nonlinear preferential rewiring’s parameters on performance. Simulation results show that various non-scale-free networks with different network topologies generated by WS model, including random networks and various networks between regular and random, are turned into scale-free networks perfectly by nonlinear preferential rewiring method.

TIME-VARYING EPIDEMIC TRANSMISSION IN HETEROGENEOUS NETWORKS AND APPLICATIONS TO MEASLES

2020 ◽  
Vol 28 (04) ◽  
pp. 901-926
Author(s):  
SARA SOTTILE ◽  
XINZHI LIU
Keyword(s):  
Heterogeneous Networks ◽  
Transmission Rate ◽  
Weighted Average ◽  
Threshold Value ◽  
Time Varying ◽  
Scale Free ◽  
Threshold Conditions ◽  
Free Network ◽  
Time Weighted Average ◽  
Stability Results

In this paper, we analyze some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends on connections between individuals, the population is modeled as a heterogeneous network. We establish some stability results related to the behavior of the time-weighted average Basic Reproduction Number (BRN). Later, a Susceptible–Exposed–Infectious–Recovered (SEIR) model which describes the measles disease is proposed and we show that its dynamics is determined by a threshold value, below which the disease dies out. Moreover, compared with models without the Exposed compartment, we can find weaker stability results. A control strategy with an imperfect vaccine is applied, to determine how it could effect the size of the peak. Due to the periodic behavior of the switching rule, we compare the results with the BRN of the model. Some simulations are given, using a scale-free network, to illustrate the threshold conditions found.

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