Stellenbosch, South Africa

**Brenda Latka**, (Program Chair), DIMACS, latka@dimacs.rutgers.edu**Wayne Getz**, UC Berkeley, getz@nature.berkeley.edu**Abba Gumel**, University of Manitoba, gumelab@cc.umanitoba.ca**Fritz Hahne**, AIMS, fjwh@aims.ac.za**John Hargrove**, SACEMA, jhargrove@sun.ac.za**Simon Levin**, Princeton University, slevin@eno.princeton.edu**Edward Lungu**, University of Botswana, lunguem@mopipi.ub.bw**Fred Roberts**, DIMACS, froberts@dimacs.rutgers.edu**Alex Welte**, Wits University, awelte@cam.wits.ac.za

This workshop is jointly organized with African Institute for Mathematical Sciences (AIMS), and

South African Centre for
Epidemiological Modelling and Analysis (SACEMA).

This workshop is jointly sponsored by:

- African Institute for Mathematical Sciences (AIMS)
- DIMACS
- US National Science Foundation
- South African Centre for Epidemiological Modelling and Analysis (SACEMA)

Title: The Impact of Local Perspectives on the Challenges Posed by Global Health Issues

I will discuss the challenges posed by globalization in a world driven primarily by local perspectives. The discussion will be driven by studies on recent outbreaks of disease like SARS, Rotavirus, HIV, Foot and Mouth Disease, Tuberculosis and Influenza. Emphasis will be put on highlighting the challenges posed by the intimate economic relationships that now exist between developing and developed nations, which have been enhanced, by travel and immigration.

Title: A Model for HIV Treatment in the Presence of HIV-Strains

Non-adherence to HAART or malabsorption of anti-HIV drugs can lead to drug-resistant HIV strains. We formulate a deterministic model that incorporates differential progression for treatment-naive, treatment susceptible and HAART-resistant infectives. First, we determine critical values of the treatment and resistance parameters that may lead to a reduction in the HIV burden. Secondly, we investigate the evolution of the drug-resistant HIV strains and ask the question: how long would it take for the proportion of individuals infected with the drug-resistant strains to exceed the WHO threshold of 5%?

Title: Intervention Impacts in Joined-Up HIV and TB Epidemics

The twin plagues of HIV and TB rate amongst the most pressing challenges of our times, with the countries of Southern Africa facing the highest burden??health systems have all but collapsed in some countries. Given the strained economies facing this mammoth challenge, one may then ask, "Is it any better (or worse) to tackle both epidemics equally than to focus on just one?" While such questions are both difficult and very unpleasant to even ask, they are necessary, and mathematics may be helpful exploring them. In this talk, a mathematical model will be used to consider the relative impacts of various management strategies, including those with a single disease focus.

Title: Does Securing Infrastructure Against Workforce-Depletion Depend on Whether the Risk is Environmental or Infectious?

Disease related work-force depletion can cause the breakdown of necessary societal infrastructure and threaten the safety of a population over and above the direct effects of serious illness. We will examine whether or not disease-related risks cause different organizational strategies to provide different levels of protection against infrastructure breakdown, depending on the nature of the disease risk (i.e. infection via environmental exposure or via contact with infected others). We will also discuss briefly how natural populations of social insects can inform and direct this research. (This talk will build upon research presented at the previous meeting, though will not presuppose knowledge of the results then shown.)

Title: Seasonality, Stochasticity and the Dynamics of Measles in the Sahel

The epidemic dynamics of measles are the best understood among acute infection. Powerful herd immunity leads to a tendency for multiannual outbreaks; these are forced mainly by seasonal variations in infection rate (due to schooling patterns in developed countries). In the Sahel, strong seasonality in transmission, correlated with the annual rains, generates high amplitude epidemics, within the chaotic region of deterministic dynamics. These erratic dynamics lead to frequent local extinction and highly asynchronous dynamics across municipalities, which present a challenge to regional control while the vaccine coverage is below herd immunity. A metapopulation model illustrates how improved vaccine coverage, below the elimination threshold, can lead to increasingly variable major outbreaks in highly seasonally forced regions. These irregular dynamics suggest an enhanced role for surveillance of population susceptibility and reactive vaccination to supplement the WHO's successful Expanded Programme for Immunization.

Title: Evaluation of Targeted Influenza Vaccination Strategies via Population Modeling

Background: Annual influenza vaccine production schedules are tight and delays frequent, with supply shortages an increasing occurrence. Absent technological innovations, vaccine supplies are unlikely to suffice for entire populations during a pandemic, especially where the mutation or reassortment facilitating person-to-person transmission of an avian or porcine strain occurs. Besides persons producing or distributing vaccine and anti-viral medications, providing health care or other critical social services, who should have priority?

Methods: In age-structured model populations, in which inter-personal contacts are proportional to age-specific activities alone or disproportionately within age groups, we compared vaccinating infants and adults aged 65+ years, the current strategy, with vaccinating schoolchildren, an oft suggested alternative.

Results: Were contacts proportional to activity, a distributed quantity peaking during childhood or adolescence that we estimate from pandemic proportions infected, vaccinating schoolchildren would mitigate mortality among the very young and old more than vaccinating them. If within-group contacts predominated, to the limit implied by reproduction numbers ≤3, infants would continue to be better protected indirectly than directly, but the impact of these strategies among adults aged 65+ years become similar. Insofar as access to health care and immune competence decline with age, the indirect strategy likely remains superior for elderly adults too.

Interpretation: Our modeling suggests, paradoxically, that those most vulnerable might best be protected by vaccinating schoolchildren. Insofar as anti-viral medications also prevent infection or reduce the duration or magnitude of infectiousness, early treatment of these super-spreaders would be most efficient, mitigating the evolution of resistance.

Title: Using Mathematics to Understand the Transmission Dynamics of HIV/AIDS and Control

Since its emergence in the 1980s, the HIV/AIDS pandemic continue to pose an unprecedented threat to global health and human development. An estimated 34-46 million people are currently living with the virus, and over 20 million people have died due to AIDS-related causes over the last two decades. In addition to the enormous socio-economic burden it imposes, AIDS is now the leading cause of death in sub-Saharan Africa, and has cut the life expectancy in a number of countries in this region. The talk will address some of the modelling issues and challenges associated with evaluating established and new strategies for curtailling the spread of HIV in Africa, such as the use of (i) antiretroviral drugs; (ii) potential (imperfect) vaccine, (iii) condom use and male circumcision. The talk will assess the impact of one other issue that is crucially important to the spread of HIV in Africa, namely the co-infection of HIV with other curable diseases such as mycobacterium tuberculosis and malaria. The talk is intended for a general audience.

Title: Thoughts on Simplifying the Estimation of HIV Incidence

Estimates of HIV-1 prevalence are the most commonly available surveillance data. However, HIV-1 incidence provides a more useful estimate of trends in the epidemic, a more sensitive indicator for evaluating the impact of prevention programs and interventions, and a more accurate prediction of the number of infected people in a population who will progress to AIDS and require comprehensive service delivery including HAART. HIV-1 incidence data are also required prior to conducting trials aimed at prevention, to provide a baseline measure, and to estimate sample size requirements. However, incidence data are rarely available because their collection requires follow-up of large cohorts, which is difficult, protracted, and expensive.

HIV incidence can also be estimated from age-stratified HIV prevalence data but this method involves a large number of assumptions regarding mortality and fertile rates, requires good age-prevalence data (which is often unavailable in Africa) and is increasingly complicated by the ART roll-out.

As an alternative to longitudinal studies, laboratory assays are being developed that distinguish people who have been infected recently from those with long-term HIV-1 infection. These assays are based on changing antibody characteristics following seroconversion. In a cross-sectional prevalence survey, the numbers of recently infected, and of HIV-1-negative, people can be used to estimate HIV-1 incidence in the population.

The various ways of estimating HIV incidence are discussed - with particular reference to the use of one of the latter laboratory-based methods, the BED capture enzyme immunoassay (BED) technique, developed by the Centers for Disease Control and Prevention (CDC).

Title: Modeling the Epidemiological and Economic Impact of HIV/AIDS with Special Reference to Zimbabwe

This is work by Vengai Runyowwa, Zindoga Mukandavira and Senelani Dorothy Hove-Musekwa, which I will present.

Title: Drug Resistance Surveillance in Subtype C HIV-1 and Evolutionary and Phylogenetic Analysis Across Time, Space and Treatment?

I am particularly interested in relating to the workshop the outcome, plans and data that should become available from the SATuRN meeting taking place on June 4,5th in Durban. The contribution that I may be able to provide would be the outcome of Durban-SATuRN, combined with recent phylogenetic modeling we have completed around the evolution of the epidemic in Zimbabwe.

Title: The Mathematical Model of HIV/AIDS Transmission: Impact of Antiretroviral Therapy

The study investigates the dynamics of the disease in a population in which treatment is administered in the symptomatic and full blown AIDS classes. The model assumes that treatment reduces the viral load and CD4+ count improves to the level of the infected individuals in the chronic stage. The analysis of the model shows that decreasing infectivity and increasing the duration of infectiveness may have the effect of increasing the pool of infection transmitters. We derive conditions under which treatment lowers the burden of HIV/AIDS. We further demonstrate numerically the theoretical results obtained from the study and make suggestions to policy makers to implement effective support structures to non-ARV infected individuals.

Title: Economic Aspects of Disease Epidemiology

Mathematical models of infectious diseases such as malaria, HIV/AIDS and schistosomiasis have given us important insights on how diseases are transmitted and how best to control them. More recently, economists have become interested in studying infectious diseases in order to understand how individuals respond to the risk of infection and how best to design and allocate resources for public health programs of prevention and treatment. Despite their common use of mathematics, and pursuit of similar questions, rarely have economists, mathematical epidemiologists and biologists collaborated in understanding how diseases evolve and spread. In this lecture we explore the benefit of incorporating simple economic principles of individual behavior and resource optimization into epidemiological models. I plan to discuss the interplay between human behavior and economic incentives and suggest important directions for future collaborations, including incorporating assumptions of rational behavior, considering externalities, and taking into account global disease commons.

Title: Optimal Control of a Discrete Time Disease Model on a Spatial Grid

An epidemic model is formulated with discrete time and spatial features. The model was formulated to model the spread of rabies in raccoons, but generalizes to other scenarios. The goal is to analyze the strategies for optimal distribution of vaccine baits to minimize the spread of the disease and the cost of implementing the control. Discrete optimal control techniques are used to derive the optimality system, which is then solved numerically to illustrate various scenarios.

Title: Emerging and Reemerging Problems in the Mathematics of Disease

The study of disease is one of the oldest areas of research in mathematical biology. This lecture will review some classical and more recent results, with emphasis on influenza, and newly emergent problems connected with the rise of antibiotic resistance.

Title: Disease Emergence in Immunocompromised Populations

Within any population, the effectiveness of individuals' immune responses to a given pathogen will vary due to many factors. In sub-Saharan Africa, the HIV/AIDS pandemic has dramatically altered population profiles of immunocompetence over recent decades, and other important factors include malnutrition and the immunological consequences of co-infection with other pathogens and parasites. Less effective immune responses may lead to increased susceptibility to infection, increased transmission rates arising from higher pathogen loads, or prolonged durations of infection; alternatively they may lead to disseminated disease and rapid host death, and hence lower infectiousness. For any disease-host system, heterogeneous host immunocompetence will cause variations in key epidemiological parameters that are correlated at the level of individual hosts. For example, more susceptible individuals may also have higher rates of transmission, or longer-lasting infections. In this presentation, I will describe the impacts of these correlated traits on the stochastic dynamics of pathogen emergence, with emphasis on acute, directly-transmitted pathogens such as influenza or SARS

Title: Making Models Useful for Policy Makers

Public health policy makers often need reliable estimates of potential impact of diseases and the possible consequences of interventions. Willingness to accept results from mathematical models, however, depends on how the modeler's) approach the problem and present the results. Typically, adoption of the results of a mathematical model as a basis for framing public health strategy and tactics is dependent upon the basic understanding of the model. This presentation will outline some guidelines, with examples, for building models that policy makers are likely to rely upon.

Title: Some Probabilistic Results on the Nonrandomness of Simple Sequence Repeats in DNA Sequences

Some probabilistic results on simple sequence repeats (SSRs) or microsatellites are derived and used to quantify the nonrandomness of SSRs as an index of nonrandomness. Applications of the index of nonrandomness are then illustrated using several examples from the literature on selected human diseased genes.

Title: Meaningless Statements in Epidemiology

A statement involving scales of measurement is called meaningless if its truth or falsity can depend on the particular versions of scales that are used in the statement. Using examples from the study of diseases such as HIV, malaria, and tuberculosis, we will give a variety of examples of meaningless and meaningful statements. We will briefly discuss the mathematical foundations of the theory of meaningfulness, discuss ways to average scores that lead to meaningful statements, and, time permitting, discuss the meaningfulness of statistical tests.

Title: New Strategies for Promoting Biomathematics in Africa

The argument I will be making is that there is need for a radical change in the education curricula in most African countries in order to create wider appreciation for Biomathematics. Currently, most of the "Biomathematicians" in Africa are individuals who are mainly "Mathematics" with little "Bio". This has its problems with regard to application of the models in the real biological world. The background is in the education systems of most African countries, which have tended to separate Mathematics from Biology at a fairly early stage.

Title: Incidence from Prevalence - Theory and Practise

While prevalence of disease is directly observed in cross sectional surveys, the incidence is difficult to measure and tends to involve costly and lengthy follow up studies. An indirect method that has received considerable recent attention is estimation of incidence from prevalence of 'recent infection'. This relationship is not in general solvable without making a number of simplifying assumptions, and it raises a number of non-trivial calibration problems. We consider a general approach and some useful special cases, and also report on the calibration of such a methodology based on data from an ongoing acute (HIV) infection cohort. This calibration is partially successful by narrow measures, but a number of difficulties are encountered and discussed.

Title: Epidemic Attractors in Periodic Environments

Demographic population dynamics are known to drive disease dynamics in constant environments. In periodic environments, we prove that demographic dynamics do not always drive disease dynamics. We exhibit a chaotic attractor in an SIS epidemic model, where the demographic dynamics are asymptotically cyclic. Periodically forced SIS epidemic models are known to exhibit multiple attractors. We prove that the basins of attraction of these coexisting attractors have infinitely many components (this is joint work with John Franke).

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Document last modified on June 4, 2007.