arXiv subjects

Joel C. Miller

Publications and source records attributed to Joel C. Miller.

27 records · Page 2Linked to original sources

arXiv2012

Co-circulation of infectious diseases on networks

We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a disease-specific rate. Infection by one disease confers immediate and permanent immunity to infection by any disease. Under these assumptions, we find a simple, low-dimensional ordinary differential equations model which captures the global dynamics of the infection. The dynamics depend strongly on initial conditions. Although we motivate this article with infectious disease, the model may be adapted to the spread of other infectious agents such as competing political beliefs, rumors, or adoption of new technologies if these are influenced by contacts. As an example, we demonstrate how to model an infectious disease which can be prevented by a behavior change.

q-bio.PE↗

arXiv2012

Epidemics on networks with large initial conditions or changing structure

Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The models do not apply if the initial proportion is large (and fail whenever R_0<1), and cannot measure the impact of an intervention. Methods: In this paper we adapt "edge-based compartmental models" to situations having finite-sized initial conditions. Results: The resulting models remain simple and accurately capture the effect of the initial conditions. It is possible to generalize the model to networks whose partnerships change in time. Conclusions: The resulting models can be applied to a range of important contexts. The models can be used to choose between different interventions that affect the disease or the population structure.

q-bio.PE↗

arXiv2011

Edge-based compartmental modeling for epidemic spread Part II: Model Selection and Hierarchies

We consider the edge-based compartmental models for epidemic spread developed in Part I. We show conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the Mass Action model gives clear, rigorous conditions under which the Mass Action model is accurate.

q-bio.PE↗

arXiv2011

Edge-Based Compartmental Modeling for Infectious Disease Spread Part I: An Overview

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes all individuals have the same contact rate and contacts are fleeting. This paper is the first of three investigating edge-based compartmental modeling, a technique eliminating these assumptions. In this paper, we derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of contact duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model. This paper focuses on the technique and how to apply it in different contexts. The companion papers investigate choosing the appropriate level of complexity for a model and how to apply edge-based compartmental modeling to populations with various sub-structures.

q-bio.PE↗

arXiv2011

Edge-Based Compartmental Modeling for Infectious Disease Spread Part III: Disease and Population Structure

We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of the disease or population from the simplistic assumptions of Part I. We allow the population to have structure due to effects such as demographic detail or multiple types of risk behavior the disease to have more complicated natural history. We introduce these modifications in the static network context, though it is straightforward to incorporate them into dynamic networks. We also consider serosorting, which requires using the dynamic network models. The basic methods we use to derive these generalizations are widely applicable, and so it is straightforward to introduce many other generalizations not considered here.

q-bio.PE↗

arXiv2009

A note on a paper by Erik Volz [arXiv:0705.2092]: SIR dynamics in random networks

Recent work by Erik Volz [arXiv:0705.2092] has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to account for effects due to heterogeneity in degree that are neglected in the standard mass-action SIR equations. In this note we offer an alternate derivation which arrives at a simpler -- though equivalent -- system of governing equations to that of Volz. This new derivation is more closely connected to the underlying physical processes, and the resulting equations are of comparable complexity to the mass-action SIR equations. We further show that earlier derivations of the final size of epidemics on networks can be reproduced using the same approach, thereby providing a common framework for calculating both the dynamics and the final size of an epidemic spreading on a random network.

q-bio.PE↗

arXiv2008

Spread of infectious diseases through clustered populations

Networks of person-person contacts form the substrate along which infectious diseases spread. Most network-based studies of the spread focus on the impact of variations in degree (the number of contacts an individual has). However, other effects such as clustering, variations in infectiousness or susceptibility, or variations in closeness of contacts may play a significant role. We develop analytic techniques to predict how these effects alter the growth rate, probability, and size of epidemics and validate the predictions with a realistic social network. We find that (for given degree distribution and average transmissibility) clustering is the dominant factor controlling the growth rate, heterogeneity in infectiousness is the dominant factor controlling the probability of an epidemic, and heterogeneity in susceptibility is the dominant factor controlling the size of an epidemic. Edge weights (measuring closeness or duration of contacts) have impact only if correlations exist between different edges. Combined, these effects can play a minor role in reinforcing one another, with the impact of clustering largest when the population is maximally heterogeneous or if the closer contacts are also strongly clustered. Our most significant contribution is a systematic way to address clustering in infectious disease models, and our results have a number of implications for the design of interventions.

q-bio.QM↗

arXiv2008

Bounding the Size and Probability of Epidemics on Networks

We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of a node to be the marginal probability that it would infect a randomly chosen neighbor given its infectiousness and the distribution of susceptibility. For a given distribution of out-transmissibility, we find the conditions which give the upper [or lower] bounds on size and probability of an epidemic, under weak assumptions on the transmission properties, but very general assumptions on the network. We find similar bounds for a given distribution of in-transmissibility (the marginal probability of being infected by a neighbor). We also find conditions giving global upper bounds on size and probability. The distributions leading to these bounds are network-independent. In the special case of networks with high girth (locally tree-like), we are able to prove stronger results. In general the probability and size of epidemics are maximal when the population is homogeneous and minimal when the variance of in- or out-transmissibility is maximal.

q-bio.PE↗

arXiv2007

Predicting the size and probability of epidemics in a population with heterogeneous infectiousness and susceptibility

We analytically address disease outbreaks in large, random networks with heterogeneous infectivity and susceptibility. The transmissibility $T_{uv}$ (the probability that infection of $u$ causes infection of $v$) depends on the infectivity of $u$ and the susceptibility of $v$. Initially a single node is infected, following which a large-scale epidemic may or may not occur. We use a generating function approach to study how heterogeneity affects the probability that an epidemic occurs and, if one occurs, its attack rate (the fraction infected). For fixed average transmissibility, we find upper and lower bounds on these. An epidemic is most likely if infectivity is homogeneous and least likely if the variance of infectivity is maximized. Similarly, the attack rate is largest if susceptibility is homogeneous and smallest if the variance is maximized. We further show that heterogeneity in infectious period is important, contrary to assumptions of previous studies. We confirm our theoretical predictions by simulation. Our results have implications for control strategy design and identification of populations at higher risk from an epidemic.

q-bio.QM↗