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 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.

Interplay of epidemic spreading and strategy-mixed awareness diffusion on multiplex networks

2020 ◽  
Vol 31 (06) ◽  
pp. 2050085
Author(s):  
Jia-Qian Kan ◽  
Chuang Ma ◽  
Hai-Feng Zhang ◽  
Bing-Bing Xiang
Keyword(s):  
Diffusion Mechanism ◽  
Contact Layer ◽  
Physical Contact ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Multiplex Networks ◽  
Markov Chain Approach ◽  
Epidemic Size ◽  
Final Epidemic Size ◽  
Local Awareness

In this paper, the interplay of epidemic spreading and the strategy-mixed awareness diffusion within the framework of multiplex networks is studied. In the model, epidemics can spread through a physical-contact layer and the awareness can diffuse through a virtual-contact layer. Each node on physical-contact layer is randomly matched one-to-one with a node of virtual-contact layer, but the connectivity is distinct in each of them. In view of the complexity of human behaviors, we assume that the diffusion of awareness is ruled by two mixed contagion dynamics: a fraction [Formula: see text] of individuals adopt the herd-like dynamics and the others follow the epidemic-like dynamics. We analyze the epidemic threshold based on the microscopic Markov chain approach. Meanwhile, combing with the Monte Carlo (MC) simulations, we show that the strategy-mixed awareness diffusion mechanism can enrich the dynamics of epidemic spreading, including the crossover phenomenon of the final epidemic size, the two-stage effect of the local awareness rate, and so forth.

An edge-based model for non-Markovian sexually transmitted infections in coupled network

2020 ◽  
Vol 13 (02) ◽  
pp. 2050014
Author(s):  
Xiaofeng Luo ◽  
Junyuan Yang ◽  
Zhen Jin ◽  
Jia Li
Keyword(s):  
Single Layer ◽  
Recovery Process ◽  
Heterosexual Transmission ◽  
Bipartite Networks ◽  
Epidemic Threshold ◽  
Sexually Transmitted ◽  
Epidemic Size ◽  
Recovery Times ◽  
Age Structured ◽  
Edge Based

In this paper, allowing for general transmission and recovery times distributions, we proposed an edge-based age-structured-like compartmental model for STIs (EBACMS) in a coupled network. We considered sexual transmissions between men with also heterosexual contacts. Mathematically, we gave the general approach of proving the nonnegativity of solutions for the system coupling ordinary and partial differential equations, which can be applied to all edge-based compartment models. We then analyzed the epidemic threshold [Formula: see text] with different distributions which couples the thresholds of the single-layer and bipartite networks in the percolation theory. We also studied the global stability of disease-free equilibrium with [Formula: see text] and the final epidemic size [Formula: see text] (the proportion of the population experiencing infection during the epidemic) with [Formula: see text]. In addition, numerical simulations indicated that given a fixed exponential transmission distribution, a higher variance (with same mean) in general recovery distribution gives smaller [Formula: see text] and [Formula: see text]. Sensitivity analysis on [Formula: see text] and [Formula: see text] in terms of the parameters illustrated that male-to-male transmission routes have a greater impact on [Formula: see text] and [Formula: see text] than the heterosexual transmission routes for the Markovian transmission process and arbitrary recovery process. The results provide a good theoretical guideline to consider the distributions of real-world STIs.

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 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.

Epidemic spreading on evolving networks

2019 ◽  
Vol 33 (23) ◽  
pp. 1950266 ◽  
Author(s):  
Jin-Xuan Yang
Keyword(s):  
Preferential Attachment ◽  
Small World ◽  
Network Evolution ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Scale Free ◽  
Evolving Networks ◽  
Power Law Exponent ◽  
Free Network ◽  
Over Time

Network structure will evolve over time, which will lead to changes in the spread of the epidemic. In this work, a network evolution model based on the principle of preferential attachment is proposed. The network will evolve into a scale-free network with a power-law exponent between 2 and 3 by our model, where the exponent is determined by the evolution parameters. We analyze the epidemic spreading process as the network evolves from a small-world one to a scale-free one, including the changes in epidemic threshold over time. The condition of epidemic threshold to increase is given with the evolution processes. The simulated results of real-world networks and synthetic networks show that as the network evolves at a low evolution rate, it is more conducive to preventing epidemic spreading.

scholarly journals Antiviral treatment for the control of pandemic influenza: some logistical constraints

2007 ◽  
Vol 5 (22) ◽  
pp. 545-553 ◽  
Author(s):  
N Arinaminpathy ◽  
A.R McLean
Keyword(s):  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Size ◽  
Conservative Policy ◽  
Control Programmes ◽  
Final Epidemic Size ◽  
Number Of Treatment ◽  
Modelling Approach

Disease control programmes for an influenza pandemic will rely initially on the deployment of antiviral drugs such as Tamiflu, until a vaccine becomes available. However, such control programmes may be severely hampered by logistical constraints such as a finite stockpile of drugs and a limit on the distribution rate. We study the effects of such constraints using a compartmental modelling approach. We find that the most aggressive possible antiviral programme minimizes the final epidemic size, even if this should lead to premature stockpile run-out. Moreover, if the basic reproductive number R 0 is not too high, such a policy can avoid run-out altogether. However, where run-out would occur, such benefits must be weighed against the possibility of a higher epidemic peak than if a more conservative policy were followed. Where there is a maximum number of treatment courses that can be dispensed per day, reflecting a manpower limit on antiviral distribution, our results suggest that such a constraint is unlikely to have a significant impact (i.e. increasing the final epidemic size by more than 10%), as long as drug courses sufficient to treat at least 6% of the population can be dispensed per day.

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.

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

1998 ◽  
Vol 35 (03) ◽  
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.

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