A Network Epidemic Model with Preventive Rewiring: Comparative Analysis of the Initial Phase

Britton, Tom; Juher, David; Saldaña, Joan

doi:10.1007/s11538-016-0227-4

Cited by 18 publications

(34 citation statements)

References 36 publications

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“…agreeing with Britton et al [17], equation (3). The basic reproduction number R 0 is obtained from (5.22) by evaluating the right hand side at λ = 0, yielding the same expression as (2.1).…”

Section: Connection To Other Approachessupporting

confidence: 92%

“…Britton et al [17] and Jacobsen et al [22]). Our work takes the model introduced in Britton et al [17] as its starting point. Britton et al [17] consider a broader class of models but restrict the analysis to the initial phase of the epidemic.…”

Section: Introductionmentioning

confidence: 97%

“…In this section we define the stochastic SIR network epidemic model with preventive dropping. This model is a special case of the network epidemic model with preventive rewiring defined in Britton et al [17], namely where there is no latency period and where the fraction of dropped edges that are replaced by new edges is set to zero. The population consists of N individuals, labelled 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

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A stochastic SIR network epidemic model with preventive dropping of edges

et al. 2019

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A Markovian Susceptible Infectious Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size , assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy–Reed (in which the degrees of individuals are deterministic) and Newman–Strogatz–Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman–Strogatz–Watts version. The basic reproduction number and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when , the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the size of the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N .

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Section: Connection To Other Approachessupporting

confidence: 92%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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A stochastic SIR network epidemic model with preventive dropping of edges

et al. 2019

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“…Owing to stochastic effects, it is always possible that an epidemic dies out when introduced into a population (with finite size n) even when R 0 > 1. Previous work ( [20]; see also SI Section S1.2 ) showed that the basic reproduction number R 0 for the epidemic on the configuration network with social distancing is given by…”

Section: 3mentioning

confidence: 99%

Individual preventive social distancing during an epidemic may have negative population-level outcomes

Leung

Ball

Sirl

et al. 2018

J. R. Soc. Interface.

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The outbreak of an infectious disease in a human population can lead to individuals responding with preventive measures in an attempt to avoid getting infected. This leads to changes in contact patterns. However, as we show in this paper, rational behaviour at the individual level, such as social distancing from infectious contacts, may not always be beneficial for the population as a whole. We use epidemic network models to demonstrate the potential negative consequences at the population level. We take into account the social structure of the population through several network models. As the epidemic evolves, susceptible individuals may distance themselves from their infectious contacts. Some individuals replace their lost social connections by seeking new ties. If social distancing occurs at a high rate at the beginning of an epidemic, then this can prevent an outbreak from occurring. However, we show that moderate social distancing can worsen the disease outcome, both in the initial phase of an outbreak and the final epidemic size. Moreover, the same negative effect can arise in real-world networks. Our results suggest that one needs to be careful when targeting behavioural changes as they could potentially the epidemic outcome. Furthermore, network structure crucially influences the way that individual-level measures impact the epidemic at the population level. These findings highlight the importance of careful analysis of preventive measures in epidemic models.

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“…Using SIS and SIR epidemic models on configuration model networks, Britton et al [97] studied the impact of social distancing on the early stages of an outbreak. In particular, they considered preventive rewiring , in which susceptible individuals break off contacts with infectious individuals at a specified rate and replace those contacts with non-infectious individuals.…”

Section: Mechanistic Models Representing Epidemic Growth Profilesmentioning

confidence: 99%

Mathematical models to characterize early epidemic growth: A review

Chowell

Sattenspiel

Bansal

et al. 2016

Physics of Life Reviews

403

393

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There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa.

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A Network Epidemic Model with Preventive Rewiring: Comparative Analysis of the Initial Phase

Cited by 18 publications

References 36 publications

A stochastic SIR network epidemic model with preventive dropping of edges

A stochastic SIR network epidemic model with preventive dropping of edges

Individual preventive social distancing during an epidemic may have negative population-level outcomes

Mathematical models to characterize early epidemic growth: A review

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