A precise definition of the basic reproduction number, Ro, is presented for a general compartmental disease transmission model based on a system of ordinary dierential equations. It is shown that, if Ro 1, then it is unstable. Thus,Ro is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for Ro near one. This criterion, together with the definition of Ro, is illustrated by treatment, multigroup, staged progression, multistrain and vectorhost models and can be applied to more complex models. The results are significant for disease control.

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Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

Background Antiretroviral therapy that reduces viral replication could limit the transmission of human immunodeficiency virus type 1 (HIV-1) in serodiscordant couples. Methods In nine countries, we...

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Prevention of HIV-1 Infection with Early Antiretroviral Therapy

The study subjects were followed for 3324 person-years (median, 1.2 years; maximum, 2.8 years). Of these subjects, 10 were found to have been infected with HIV at en rollment, and 100 became infected during follow-up (36 in the FTC–TDF group and 64 in the placebo group), indicating a 44% reduction in the incidence of HIV (95% confidence interval, 15 to 63; P = 0.005). In the FTC–TDF group, the study drug was detected in 22 of 43 of seronegative subjects (51%) and in 3 of 34 HIV-infected subjects (9%) (P<0.001). Nausea was reported more frequently during the first 4 weeks in the FTC–TDF group than in the placebo group (P<0.001). The two groups had similar rates of serious adverse events (P = 0.57). Conclusions Oral FTC–TDF provided protection against the acquisition of HIV infection among the subjects. Detectable blood levels strongly correlated with the prophylactic effect. (Funded by the National Institutes of Health and the Bill and Melinda Gates Foun dation; ClinicalTrials.gov number, NCT00458393.)

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Preexposure Chemoprophylaxis for HIV Prevention in Men Who Have Sex with Men

By Matthew James Keelingand Pejman RohaniPrinceton, NJ: Princeton University Press,2008.408 pp., Illustrated. $65.00 (hardcover).Mathematical modeling of infectious dis-eases has progressed dramatically over thepast 3 decades and continues to ﬂourishat the nexus of mathematics, epidemiol-ogy, and infectious diseases research. Nowrecognized as a valuable tool, mathemat-ical models are being integrated into thepublic health decision-making processmore than ever before. However, despiterapid advancements in this area, a formaltraining program for mathematical mod-eling is lacking, and there are very fewbooks suitable for a broad readership. Tosupport this bridging science, a commonlanguage that is understood in all con-tributing disciplines is required.

Modeling Infectious Diseases in Humans and Animals

Background Antiretroviral preexposure prophylaxis is a promising approach for preventing human immunodeficiency virus type 1 (HIV-1) infection in heterosexual populations. Methods We conducted a randomized trial of oral antiretroviral therapy for use as preexposure prophylaxis among HIV-1–serodiscordant heterosexual couples from Kenya and Uganda. The HIV-1–seronegative partner in each couple was randomly assigned to one of three study regimens — once-daily tenofovir (TDF), combination tenofovir–emtricitabine (TDF–FTC), or matching placebo — and followed monthly for up to 36 months. At enrollment, the HIV-1–seropositive partners were not eligible for antiretroviral therapy, according to national guidelines. All couples received standard HIV-1 treatment and prevention services. Results We enrolled 4758 couples, of whom 4747 were followed: 1584 randomly assigned to TDF, 1579 to TDF–FTC, and 1584 to placebo. For 62% of the couples followed, the HIV-1–seronegative partner was male. Among HIV-1–seropositive par...

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Antiretroviral prophylaxis for HIV prevention in heterosexual men and women.

Summary HIV transmission models have become very complex. The behavior of some of these models may only be explored by uncertainty and sensitivity analyses, because the structural complexity of the model are coupled with a high degree of uncertainty in estimating the values of the input parameters. Uncertainty analysis may be used to assess the variability (prediction imprecision) in the outcome variable that is due to the uncertainty in estimating the input values. A sensitivity analysis can extend an uncertainty analysis by identifying which parameters are important in contributing to the prediction imprecision (i.e., how do changes in the values of the input parameters alter the value of the outcome variable). In this paper an uncertainty and a sensitivity analysis are described and applied; both analyses are based upon the Latin Hypercube Sampling (LHS) scheme, which is an extremely efficient sampling design proposed by McKay, Conover & Beckman (1979). The methods described in this paper have not previously been applied to deterministic models of disease transmission, although these models have many characteristics in common with the risk assessment models that the strategies were designed to investigate. The utility of the LHS uncertainty and the LHS/PRC (Latin Hypercube Sampling/Partial Rank Correlation) sensitivity analysis techniques are illustrated by analyzing a complex deterministic model of HIV transmission.

http://www.jstor.org/stable/pdfplus/1403510.pdf

Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an Example

In developed countries the major tuberculosis epidemics declined long before the disease became curable in the 1940s. We present a theoretical framework for assessing the intrinsic transmission dynamics of tuberculosis. We demonstrate that it takes one to several hundred years for a tuberculosis epidemic to rise, fall and reach a stable endemic level. Our results suggest that some of the decline of tuberculosis is simply due to the natural behaviour of an epidemic. Although other factors must also have contributed to the decline, these causal factors were constrained to operate within the slow response time dictated by the intrinsic dynamics.

The intrinsic transmission dynamics of tuberculosis epidemics.

The effect of antiretroviral therapy (ART) in preventing human immunodeficiency virus (HIV) infections and averting acquired immunodeficiency syndrome (AIDS) deaths in the San Francisco gay community over the next 10 years was predicted. A transmission model was coupled with a statistical approach that enabled inclusion of a high degree of uncertainty in the potential treatment effects of ART (in terms of infectivity and survival), increase in risky behavior, and rate of emergence of drug resistance. Increasing the usage of ART in San Francisco would decrease the AIDS death rate and could substantially reduce the incidence rate.

A tale of two futures: HIV and antiretroviral therapy in San Francisco.

Here we present a review of the literature of influenza modeling studies, and discuss how these models can provide insights into the future of the currently circulating novel strain of influenza A (H1N1), formerly known as swine flu. We discuss how the feasibility of controlling an epidemic critically depends on the value of the Basic Reproduction Number (R0). The R0 for novel influenza A (H1N1) has recently been estimated to be between 1.4 and 1.6. This value is below values of R0 estimated for the 1918–1919 pandemic strain (mean R0~2: range 1.4 to 2.8) and is comparable to R0 values estimated for seasonal strains of influenza (mean R0 1.3: range 0.9 to 2.1). By reviewing results from previous modeling studies we conclude it is theoretically possible that a pandemic of H1N1 could be contained. However it may not be feasible, even in resource-rich countries, to achieve the necessary levels of vaccination and treatment for control. As a recent modeling study has shown, a global cooperative strategy will be essential in order to control a pandemic. This strategy will require resource-rich countries to share their vaccines and antivirals with resource-constrained and resource-poor countries. We conclude our review by discussing the necessity of developing new biologically complex models. We suggest that these models should simultaneously track the transmission dynamics of multiple strains of influenza in bird, pig and human populations. Such models could be critical for identifying effective new interventions, and informing pandemic preparedness planning. Finally, we show that by modeling cross-species transmission it may be possible to predict the emergence of pandemic strains of influenza.

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Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)

Tuberculosis, although preventable and curable, causes more adult deaths than any other infectious disease. A theoretical framework for designing effective control strategies is developed and used to determine treatment levels for eradication, to assess the effects of noneradicating control, and to examine the global goals of the World Health Organization. The theory is extended to assess how suboptimal control programs contribute to the evolution of drug resistance. A new evaluation criterion is defined and used to suggest how control strategies can be improved. In order to control tuberculosis, treatment failure rates must be lower in developing countries than in developed countries.

https://science.sciencemag.org/content/sci/273/5274/497.full.pdf

Sally Blower

Papers

Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an Example

The intrinsic transmission dynamics of tuberculosis epidemics.

A tale of two futures: HIV and antiretroviral therapy in San Francisco.

Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)

Control Strategies for Tuberculosis Epidemics: New Models for Old Problems