How bad can it get? bounding worst case endemic heterogenous mixing models of HIV/AIDS

Kaplan, Edward H.; Lee, Yew Sing

doi:10.1016/0025-5564(90)90002-g

Cited by 36 publications

(18 citation statements)

References 24 publications

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“…The costs of avoidable morbidity and mortality due to inadequate public health response are high. Some researchers therefore suggest it is prudent to use the well-mixed DE model, where diffusion is fastest, as a worst case limit (Kaplan and Lee 1990;Kaplan 1991 Most important, the results reported here assume fixed parameters including network structure, contact rates and infectivities. All are actually endogenous.…”

Section: Network Structurementioning

confidence: 99%

Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models

2008

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When is it better to use agent based (AB) models, and when should differential equation (DE) models be used? Where DE models assume homogeneity and perfect mixing within compartments, AB models can capture heterogeneity in agent attributes and in the network of interactions among them. Using contagious disease as an example, we contrast the dynamics of AB models with those of the corresponding mean-field DE model, specifically, comparing the standard SEIR model-a nonlinear DE-to an explicit AB model of the same system. We examine both agent heterogeneity and the impact of different network structures, including fully connected, random, Watts-Strogatz small world, scale-free, and lattice networks. Surprisingly, in many conditions the AB and DE dynamics are quite similar. Differences between the DE and AB models are not statistically significant on key metrics relevant to public health, including diffusion speed, peak load on health services infrastructure and total disease burden. We explore the conditions under which the AB and DE dynamics differ, and consider implications for managing infectious disease. The results extend beyond epidemiology: from innovation adoption to the spread of rumor and riot to financial panics, many important social phenomena involve analogous processes of diffusion and social contagion.

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Section: Network Structurementioning

confidence: 99%

Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models

2008

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“…Many models have been formulated to account for this [14,47,140]. Following Jacquez et al [136] we partition the population into n groups based on sexual activity level, so that group i has on average c i partners per unit time.…”

Section: Multiple Groups: Hiv In Heterogeneous Male Homosexual Communmentioning

confidence: 99%

Dynamics of infectious diseases

et al. 2014

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Modern infectious disease epidemiology has a strong history of using mathematics both for prediction and to gain a deeper understanding. However the study of infectious diseases is a highly interdisciplinary subject requiring insights from multiple disciplines, in particular a biological knowledge of the pathogen, a statistical description of the available data and a mathematical framework for prediction. Here we begin with the basic building blocks of infectious disease epidemiologythe SIS and SIR type models -before considering the progress that has been made over the recent decades and the challenges that lie ahead. Throughout we focus on the understanding that can be developed from relatively simple models, although accurate prediction will inevitably require far greater complexity beyond the scope of this review. In particular, we focus on three critical aspects of infectious disease models that we feel fundamentally shape their dynamics: heterogeneously structured populations; stochasticity; and spatial structure. Throughout we relate the mathematical models and their results to a variety of real-world problems.

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“…Equation (4), dubbed the law of conservation of sex, ensures that the aggregate number of sex partners selected from group j by members of group i equals the aggregate number of sex partners selected from group i by members of group j (or, it takes two to tango!). Kaplan and Lee (1990) present arguments demonstrating the generality of these four equations (which may not be apparent). For now, note that it is not necessary to assume that the AIDS incubation time is exponentially distributed with mean lly.…”

Section: Bounding Worst Case Sexual Mixing Models Of Hiv Transmissionmentioning

confidence: 95%

“…For now, note that it is not necessary to assume that the AIDS incubation time is exponentially distributed with mean lly. As shown in Kaplan and Lee (1990), if the survivor function for the AIDS incubation time is denoted by Pr{ A>t}, then the average remaining time spent in the population by a newly infected person is given by = I e Mt Pr{A>t} dt (5) '0 and the parameter y is thus found by equating…”

Section: Bounding Worst Case Sexual Mixing Models Of Hiv Transmissionmentioning

confidence: 99%

“…In this paper, the endemic worst case problem will be defined, and the procedure recently developed by Kaplan and Lee (1990) for placing an upper bound on the number of infected persons will be summarized (the reader is referred to Kaplan & Lee, 1990, for the mathematical details). Following this summary, realistic epidemiological and behavioral parameters gleaned from studies of the AIDS epidemic in San Francisco are presented.…”

Section: Introductionmentioning

confidence: 99%

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Worst case analysis of sexual mixing models of HIV transmission

Kaplan

1991

Journal of Sex Research

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The sexual transmission of HIV/AIDS depends upon the specifics of mixing between subpopulations with differing sexual activity rates. As the manner in which such mixing occurs is very difficult to observe, it is natural to consider the number of infected persons that would result from worst case mixing, that is, mixing that maximizes the number of infected persons in the population. This paper summarizes a recently developed procedure for producing a tight upper bound on the maximum number of infected persons in a population over the long run within the assumptions of a fairly general model of HIV transmission. The technique is illustrated utilizing parameters derived from studies of the AIDS epidemic in San Francisco. An example demonstrating how one might prospectively evaluate an AIDS intervention program using worst case analysis is also discussed.

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How bad can it get? bounding worst case endemic heterogenous mixing models of HIV/AIDS

Cited by 36 publications

References 24 publications

Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models

Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models

Dynamics of infectious diseases

Worst case analysis of sexual mixing models of HIV transmission

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