This workshop is jointly organized with African Institute for Mathematical Sciences (AIMS),
South African Centre for Epidemiological Modelling and Analysis (SACEMA) and University of the Witwatersrand, Johannesburg.
This workshop is jointly sponsored by:
Title: SARS Outbreaks in Toronto, Hong Kong and Singapore: The Role of Diagnosis and Isolation as a Control Mechanism
We use a compartmental epidemic model to describe the transmission dynamics of Severe Acute Respiratory Syndrome (SARS) in Toronto, Hong Kong and Singapore. The mean number of secondary cases generated by a primary SARS case during its period of infectiousness (known as the reproduction number) is estimated from timeseries data of the early epidemic phase. We also evaluate the role of rapid diagnosis and effective isolation of infectious individuals in hospitals as control mechanisms. An uncertainty and sensitivity analysis on the reproduction number is also carried out using independent epidemiological estimates obtained from SARS-patient records in Hong Kong.
Title: Maternal Herpes Simplex Virus Type 2 Infection and Risk of Intra-Partum Transmission of HIV: Results of a Nested Case Control Study
Background - Herpes simplex virus type 2 (HSV-2) facilitates sexual transmission of HIV. The effect of maternal HSV-2 co-infection on intra-partum mother-to-child-transmission (MTCT) of HIV is unknown. >p>Methods - In a nested case-control study using archived sera from ZVITAMBO, an MTCT trial, rates of prevalent and incident HSV-2 infection and syphilis were compared between 509 HIV-positive women who transmitted HIV to their infants during the intra-partum period and 1018 HIV-positive women whose infants remained HIV-uninfected at one year of age. Maternal sera collected < 96 hours of delivery, and 6-week samples from baseline HIV-negative women were tested for HSV-2 antibody. Six-week samples were also tested for syphilis using RPR and TPHA. TPHA?positive women with RPR >1:8 were presumed to have active/incubating syphilis at delivery.
Findings - Prevalence of maternal HSV-2 at delivery was 82.5% (95% CI 80.6-84.5) and 4.0% (95% CI 3.0-5.1). HSV-2 incidence by 6 weeks was 17.3% (95% CI 11.3-23.3). Prevalent HSV-2 infection was associated with increased intra-partum HIV transmission (adjusted odds ratio: 1.50 [95% CI 1.09-2.08]). The proportion of intra-partum transmissions potentially attributable to prevalent HSV-2 infection was 28.4% (95% CI: 7.3-44.7). Women who became HSV-2 infected around the time of delivery also appeared to be at increased risk of intra-partum HIV transmission (adjusted OR: 1.44 [0.57-3.69]).
Interpretation - HSV-2 infection is common among HIV-positive women and associated with an increased risk of intra-partum HIV MTCT. More than 25% of intra-partum HIV MTCT may be attributable to maternal HSV-2 co-infection. HSV-2 acquisition during the peri-partum period was common.
Title: Spatial Coherence and the Association of Temperature, Rainfall with the Incidence of Dengue Hemorrhagic Fever
The seasonal increase in dengue hemorrhagic fever in Thailand is often cited as occurring concomitantly with the warm, rainy season. We have investigated this relationship in detail to determine if the seasonal variance in incidence is associated with seasonal variance in temperature and rainfall across Thailand. Using a time-series decomposition technique, the empirical mode decomposition, we examine the seasonal variance of DHF, rainfall and temperature in a large dataset describing monthly DHF incidence, mean monthly temperature and monthly rainfall in 41 provinces for 14 years. The empirical mode decomposition sifts time-series data into modes of different periodicities. Using the non-parametric spline covariance function, we find that temperature is synchronized across the country while DHF incidence and rainfall vary markedly in phase in different parts of the country. Phase coherence analysis of DHF incidence and rainfall suggests that the timing of the dengue season is linked to the timing of rainfall across Thailand. Additionally, we have found that annual DHF incidence rates are associated with higher mean annual temperatures. This relationship is modified by the distance from Bangkok, with provinces close to Bangkok varying little with varying temperature, while those furthest from Bangkok are more strongly associated with temperature. This modification of the effect of temperature suggests that several processes at different temporal and spatial scales affect incidence across the country.
Title: Models of New Vaccines for Measles
Despite the availability of an effective vaccine, measles continues to cause a substantial amount of morbidity and mortality globally and especially in Africa. One strategy for reducing this burden is to develop new vaccines that can be delivered at younger ages. The current vaccine does not induce effective immunity in children younger than nine months of age. A vaccine that could be given to younger children would reduce the reservoir of children who are not protected by waning maternal immunity and are not yet vaccinated. Such a vaccine would not only potentially reduce morbidity and mortality in this age group but also increase the probability of elimination of the disease altogether in some settings. However, the specific benefit of these vaccines is not known even if they were available. Using an age-specific simulation model, we quantify the potential benefit of vaccines that can be delivered at younger ages both in terms of the reduction of morbidity and mortality and in increasing the probability of elimination of disease.
Title: Conjoined Epidemics: a New Problem for Southern Africa
There have been several oppressive developments in public health. The obsessive pursuit of treatment of established disease consumes almost all the available resources. A highly centralized bureaucracy effectively restricts freedom of action. Rural health professionals work without support. Politicians and human rights lawyers have usurped a public health function.
The countries of Southern Africa face an unprecedented public health debacle. Control of the conjoined epidemics of tuberculosis and HIV/AIDS requires a complete break with the past and, in particular with the baggage accumulated around HIV and tuberculosis in South Africa in the past decade. The following questions will be discussed:
What is driving the epidemic of tuberculosis? What do we need to do in order not to fall into the trap of doing more of the same and failing again?
Analysis of Zimbabwes policies will be given and recommendations for South Africa made, including the fundamental one of developing a strong partnership between epidemiological modeling and the application of public health strategies. Public health interventions need to be evaluated against a properly constructed mathematical model, which will tell us exactly where we are going and how fast.
Title: Overview of the State of Infectious Diseases in South Africa
The talk will present an overview of the state of infectious disease in Southern Africa, with emphasis on problems, challenges, new initiatives, social costs of disease, etc. Comments will be added about ways that the medical community and modelers can work together.
Title: A Cost-Effectiveness Analysis of Alternative HPV Vaccination Strategies
The objective of this study was to assess the cost-effectiveness of alternative HPV vaccination strategies in settings with established cervical cancer screening programs in the United States. A non-linear, deterministic, mathematical model of the transmission dynamics of HPV infection (6,11,16,18) and disease development in an age-structured population was developed and integrated with an economic model. Inputs for the model were obtained from public data sources, published literature, and clinical trials. Compared with current practice, vaccinating females and males before the age of 12 augmented by a 12-24-year olds temporary catch-up program was the most effective strategy, substantially reducing the incidence of genital warts, cervical intraepithelial neoplasia (CIN), and cervical cancer. Vaccination with a quadrivalent HPV vaccine can provide survival benefits and quality of life improvements, and is potentially cost-effective for a reasonably wide range of model input values.
Title: Preparing Societal Infrastructure Against Disease-Related Workforce Depletion
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 discuss a few preliminary models examining how to plan ahead: where redundancies in the training of a workforce and in workforce deployment in critical positions can increase the robustness of the society to be able to better withstand these threats. Time permitting, we will discuss how such planning should change to reflect the threat posed by the disease itself (e.g. seasonal depletion from Malaria, or growing constantly from AIDS).
Title: Evaluating the Potential Burden of Zoonotic Mycobacteria in Africa: Can Modelling Disease in Wildlife Populations Help?
Mycobacterium tuberculosis (TB) is an ancient disease with a global distribution. Despite attempts to curtail its spread, annual incidence levels continue to rise, which has resulted in over one-third of the global human population contracting the disease. Over 95% of annual global TB cases are reported from developing countries alone, leading to over 3 million associated deaths. Consequently, tuberculosis eradication is considered to be one of the foremost public health priorities of the 21st Century.
Bovine tuberculosis, (M. bovis, BTB) is a similar pathogen with an equally wide geographical distribution. It affects a wide range of wildlife and domestic animals, including threatened and economically valuable species. Despite being listed as animal health priority by the Office International des Epizooties, appropriate data is unavailable for many developing nations. As BTB has the capacity to act as a zoonotic pathogen, human populations that are closely associated with infected animals face an increased risk of infection via aerosol and food borne transmission.
Although the World Health Organisation first recognised BTB as a public health concern in 1950, very few studies have addressed the quantitative aspects of the disease burden in humans. Current data suggests that 80% of domestic cattle and humans in Africa reside in areas with no access to disease control programmes. As levels of drug-resistant TB and HIV infections continue to rise, quantifying the role of BTB infection in human tuberculosis patients may prove to be an important step in designing effective disease control programmes.
By analysing the spatial and temporal disease profiles of BTB in wildlife, livestock and human populations in rural communities, our study aims to quantify the role of BTB as a zoonotic disease in South Africa. This paper will present the results of our latest research on bovine tuberculosis in South African wildlife populations, and examine the opportunities that modelling may provide in understanding this infectious disease in Africa.
Title: A Model in Which Successive Infections With or Vaccinations Against Rotavirus Increase Immunity, Progressively Mitigating Symptoms (with Roger Glass, Umesh Parashar, Manish Patel, and Marc-Alain Widdowson)
Background: Rotavirus is the leading cause of severe diarrhea among young children worldwide, with mortality greatest where oral rehydration therapy is relatively inaccessible. Children who survive their initial infections may be re-infected, but successive illnesses are milder as immunity develops. Rotavirus is so ubiquitous and replicates so rapidly that very few particles are required to infect na´ve hosts. Preliminary calculations suggest R0 is higher than heretofore reported for any infectious disease. Even if the herd immunity threshold cannot be attained, vaccines that engender an immune response similar to natural infection would mitigate morbidity. Methods: To better understand the epidemiology of severe diarrhea due to rotavirus, and thereby assist in the design or evaluation and possible improvement of programs for recently or soon-to-be licensed vaccines, we modeled rotavirus transmission. Our model is a system of partial differential equations that describe transitions via infection and recovery among decreasingly susceptible (or increasingly immune) and infectious states, via vaccination among the same increasingly immune states, or combinations. We have not distinguished serotypes, but as one vaccine is mono- and other heterotypic, evidence of cross-protection would motivate this complication. Approach: We will attempt to reproduce characteristic epidemiological features of this disease such as the younger mean age of first infections in tropical than temperate regions, due either to year-round versus seasonal risk or greater force of infection accompanying less sanitary environs. Should we fail, we will identify and remedy causes of apparent disparities. On succeeding, we will assist in the design of vaccination programs. Whatever the explanation for the younger mean age at first infection, for example, doses at birth, two and four months of age might be optimal in the tropics despite interference via passively acquired maternal antibodies. In temperate regions, schedules beginning at two months of age, when infant immune systems are more mature and interference less likely, might be accelerated or supplemented via mass campaigns prior to the rotavirus season. Where vaccination has begun, we will evaluate its impact (e.g., decreased environmental contamination in the tropics might increase seasonality via respiratory transmission) and suggest means of compensating.
Title: Modeling Transmission Dynamics of HIV/AIDS: Some Results, Issues and Challenges
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 resource-poor nations. This would include the use of (i) antiretroviral therapy (universal vs targetted implementation strategy); (ii) potential (imperfect) vaccine, (iii) condoms and (iv) male circumcision. One other issue crucially important to modeling HIV spread in Africa is its interaction with other curable pathogens (opportunistic infections) such as mycobacterium tuberculosis and malaria. The key question here is whether or not the limited public health resources should be targetted to adequately containing the pathogens...instead of HIV...to achieve optimal results (measured in terms of reduction in the burden of the diseases).
The talk is intended for a general audience.
1Merck Research Laboratories, West Point, PA, USA 2The Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA 3University of Pittsburgh, Graduate School of Public Health, Pittsburgh, PA, USA 4Howard Brown Health Center and Feinberg School of Medicine Northwestern University, Chicago, IL, USA 5David Geffen School of Medicine, Los Angeles, CA, USA
Title: Estimating the Benefit of a HIV-1 Vaccine that Reduces Viral Load Set Point
Vaccines designed to induce cell-mediated immune responses against HIV-1 are being developed. Such vaccines may not provide sterilizing immunity but are likely to be associated with reduced viral set points after infection. We modeled the potential impact of a vaccine which reduces viral set point after infection using natural history data from 311 HIV-1 seroconverters. Lognormal parametric regression models were used to estimate the log median time to events of interest. Relative times(RT) were estimated for those with viral load set points of 30,000 copies/mL(reference group) versus those with lower viral set points. The time to key clinical events in the course of HIV-1 disease progression was significantly extended for those with viral set points 0.5-1.25 log10 copies/mL lower than the reference group. By quantifying the anticipated clinical benefits associated with a reduction in viral set point, these findings support the use of virologic endpoints in HIV-1 vaccine trials.
Title: Problems in African Epidemiology: How Can SACEMA Help?
Prof Hargrove will discuss various problems in the epidemiology of diseases such as HIV, TB and malaria that currently affect Africa and discuss the ways in which the newly formed South African Centre for Epidemiological Modelling and Analysis can make an impact in ameliorating their effects.
Title: Cervical Human Papillomavirus (HPV) Infection in HIV-1-Infected Pregnant Women in Zimbabwe
Background: The prevalence and type distribution of HPV among pregnant women with subtype C HIV-1 infection in Southern Africa is unknown, and the association of HPV infection with mother-to-child transmission (MTCT) of HIV-1 has not been explored.
Methods: HIV-1 (subtype C) positive pregnant women from a peri-urban high density setting in Zimbabwe were evaluated for prevalence and type of HPV infection by assays of cervical swab samples. Polymerase chain reaction (PCR) was performed followed by a generic ("consensus") HPV probe using DNA hybridization. Consensus-probe positive samples were re-probed for 29 individual HPV types and a probe mixture of 10 types. Infant HIV-1 infection status was determined by ELISA at 12-18 months and PCR assays at birth and 2-weeks.
Results: A total of 59 healthy subjects were enrolled. Two were excluded from HPV analyses because of insufficient DNA. With the generic probe, 77% (44/57) of samples were HPV- positive. Re-probing identified 25 unique HPV types in 34 women, with a high cancer risk type prevalence of 58% (33/57). Individual types HPV 58 (16-like) and 59 (18-like) were the most prevalent, each found in 9 women, followed by HPV 61 and 66, each found in 8 women. Six of 43 (13%) evaluable infants acquired HIV infection. Among mothers whose infants were infected, HPV was present in 83% (5/6); among mothers of uninfected infants, HPV was present in 74% (32/43) (P = 0.58).
Conclusions: A high proportion of HIV-positive pregnant women have cervical HPV infection with a broad diversity of HPV types and a high prevalence of those associated with increased cervical cancer risk. This preliminary assessment of HPV carriage warrants further study of HPV types, HIV cervical shedding and the association between HPV and MTCT of subtype C HIV-1.
Title: Evaluating the Predictive Power of R0 in Wildlife Populations: Dueling Timescales of Host Movement and Disease Dynamics
Wildlife populations experience qualitatively different infectious disease dynamics than human populations due to smaller group sizes and limited intergroup movement. While the basic reproductive number, R0, has traditionally been used to predict the probability of disease invasion, this application runs into trouble when used in highly structured wildlife populations. Chronic diseases are more likely to invade than acute diseases with the same R0 because the former persist in local groups long enough to allow host movement to spread the infection. We construct a discrete-time stochastic model with mechanistic host movement to investigate these dynamics. After analyzing the predictive power of R0 alone, we apply classification tree analyses to find a superior combination of measurable variables that predict disease invasion.
Title: Clonality in Plasmodium Falciparum Malaria
Background - Cerebral malaria due to Plasmodium falciparum is an overwhelmingly important cause of childhood mortality in sub-Saharan Africa, with ~2 million deaths per year among children less than 5 years of age. Meiosis, which takes place during passage through the mosquito, is a point in the life cycle with the potential for recombination between different genetically different parasites.
Methods - Two groups of P.falciparum?infected children were examined in Mali: asymptomatic children in the village of Bancoumana, and children hospitalized for cerebral malaria at the H˘pital Gabriel TourÚ in Bamako (a pediatric referral hospital for children from Bancoumana and other surrounding villages). Allotype-specific primers were used to amplify the variable (trimorphic: K1, MAD20, RO33) Block 2 region of merozoite surface protein 1 (MSP1) from parasite DNA in filter paper blots. Feeding experiments performed with gametocyte-positive subjects and laboratory-reared Anopheles gambiae mosquitoes were used to test for recombination between allotypes during passage through the mosquito vector.
Results - Parasites containing hybrid (MAD20 5'/RO33 3') sequences in Block 2 of MSP1 were more frequent among children with cerebral malaria than among asymptomatic infected controls (14 of 24 vs 6 of 73, Odds Ratio = 15.63, p << 0.001). Among children with asymptomatic P. falciparum infections, parasite densities were greater with hybrid parasites (11,844 vs 1,621 per Ál, p = 0.015). Feeding experiments with gametocyte positive subjects demonstrated recombination between the MAD20 and RO33 allotypes within Block 2 of MSP1. They also revealed three differences between the sequences of most wild-type MAD20 parasites and the MAD20/RO33 hybrids ? consistent with changes in the sixth and ninth tripeptides of Block 2 from SVA?SVT and SVA?SGG.
Conclusions - These results suggest that parasites with hybrid MAD20/RO33 sequences are more virulent in part because they produce higher parasitemias, presumably because the hybrid Block 2 sequence alters the epitope(s) presented by MSP1. Because parasites with hybrid sequences in Block 2 of MSP1 are likely to have recombinant sequences at other loci in the genome, these results suggest that there may be other sites within the genome which are also risk factors for cerebral malaria. Finally, they provide evidence for recombination under field conditions in a variable (trimorphic) region of the parasite genome and suggest that recombination at the time of meiosis in the mosquito is an important mechanism for the expansion of genetic diversity in P. falciparum, which potentially enhances the ability of the parasite to adapt to drugs, vaccines and other interventions.
Title: Insights from Economic-epidemiology
Little is known about how best to deploy scarce resources for disease control when epidemics occur in different but inter-connected regions or when individuals adapt to threat of infection by adopting protective measures. Mathematical models that capture the complex interplay between economics, human behavior, and disease ecology may be more helpful in understanding how diseases evolve and spread than models that rely on epidemiology alone. Current and new approaches to combining economics and epidemiology will be discussed.
Title: The Effects of Vertical Transmission on the Spread of HIV/AIDS in the Presence of Treatment
We consider a model involving three stages of HIV. It is known that during the first stage of HIV the virus reproduces at a rapid rate and produces perfect copies of itself (wild-type virus) as well as copies containing errors (mutated virus). During the latter stages of HIV when treatment with anti-retroviral drugs is administered some mutated viruses may resit anti-HIV drugs partly or even fully. We consider a simple model (as a first approximation) that incorporates mutations before and after anti-HIV drug therapy is started. In Sub-Sahara Africa countries where compliance to treatment is affected by low literacy and high poverty levels we ask the question: What is the future for control of HIV/AIDS in Sub-Sahara Africa?
Title: The Role of Mathematical Modelling in Epidemiology with Particular Reference to HIV/AIDS
AIDS is a fatal disease for which the cause is now known and the principal routes of trans- mission understood. Governments, public-health agencies and health-care providers must determine how best to allocate scarce resources for HIV treatment and prevention among different programs since the prospects are not good either for curative therapy or for ef- fective vaccine except, perhaps in the long run. Human disease has causal and preventive factors that can be identified through systematic investigation of different populations or subgroups of individuals within a population in different places or at different times. Math- ematical modelling of HIV infection in the individual and of the details of transmission between people and of different programs has provided a scientific framework to help deci- sion makers in predicting the outcome of different intervention programs and of highlighting problems that may arise in the future. Control of the epidemic therefore depends on pro- moting behavioural change among the subgroups of populations where infection is taking place and on optimum use of available therapy for those infected. Concepts from dynam- ical systems and epidemiology complemented by numerical simulations are applied. The role of mathematical modelling of HIV/AIDS epidemic has been highlighted and has shown that treatment of HIV-1 infection during the symptomatic phase has significantly improved patient survival. We present a two-strain HIV mathematical model that captures the dy- namics of the immune system and two HIV-1 variants under antiretroviral therapy. We explore the effects of chemotherapy on the dynamics of two viral strains and T lymphocytes with one mutant strain phenotypically resistant to drug effects. Model calculations show that there is a common pattern for CD4+ T cell count increase. There is a drastic increase of CD4+ T cells during the first few weeks of treatment, followed by a gradual increase and these increases are strictly by clonal expansion of pre-existing CD4+ T cells. Plasma HIV RNA dramatically decline to zero levels during the first week of drug administration. If drug efficacy is equal to or above a threshold efficacy, viral load remains at zero levels and if drug efficacy is less than the threshold efficacy, viral load gradually increases until it stabilizes. Viral rebound during treatment is entirely due to the recovery of CD4+ T cells. The results also reveal that there is a dynamic equilibrium between viral load and cytotoxic T lymphocyte (CTL) response in an infected individual during drug administration.
Title: HIV-RNA Sequence Prediction: A Lattice Walk Approach to Modeling Sequences of the HIV-1 RNA Structure
In this paper we present preliminary research on a random walk approach to predict (i.e., model or design) certain secondary RNA sequences. In particular we are interested in modeling secondary RNA sequences that are essential for the expression of the SL2 and SL3 domains within the HIV-1 5' UTR RNA sequence. These domains are both hairpin structures that are important for HIV genomic packaging. The overall goal of the paper is to establish a direct link between certain subsets of random walks and secondary RNA sequences of the SL2 and SL3 domains, and to create a mathematical model that predicts more stable HIV-1 RNA sequences for further functional studies in HIV research.
Title: Assessing Transmission Control Measures, Antivirals and Vaccine in Curtailing Pandemic Influenza: Scenarios for the US, UK, and South Africa
Current avian flu cases from direct contact with poultry in several regions of the world have prompted the urgency to develop pandemic preparedness plans worldwide. Leading recommendations in these plans include the use of antiviral, vaccine, and basic public health control measures for minimizing hospital (nosocomial) and community transmission (such as isolation, quarantine and social distancing). This paper presents a mathematical model for the theoretical evaluation of the pandemic flu preparedness plans of three countries, namely the US, the UK and South Africa. Single and combined interventions, consisting of the aforementioned interventions, were assessed. Using data from the USA, the study shows that hospital and community transmission control measures alone can be highly effective in reducing the impact of a potential flu pandemic. We further show that while the singular use of antivirals could results in reduction in the burden of a pandemic, the combination of transmission control measures, antivirals and vaccine is the most ``optimal'' choice. However, such an optimal strategy may not be realistically attainable at the onset of a pandemic. Consequently, other alternative (realistic) interventions need to be considered.
The study further shows, using data from the USA, UK and South Africa, that an ``optimal'' preparedness plan is largely dependent on the availability of resources. Hence, it is country--specific. For example, we show that for antiviral interventions, countries with limited resources should emphasize their use therapeutically (rather than prophylactically). However, countries with large antiviral supplies can achieve better reduction in disease burden by implementing them both prophylactically and therapeutically. This study promotes alternative strategies that may be feasible and attainable for the US, UK and South Africa. We emphasize the importance of hospital and community transmission control measures in addition to the therapeutic (and timely) use of antivirals treatment in reducing the burden of a potential flu pandemic. A program based on the use of vaccination seems to have limited impact in comparison to those based on the use or antivirals or control measures for curtailing hospital and community transmission. Although the use of antivirals as prophylaxis seems promising, such a strategy entails the use of large stockpiles that may not be available or affordable in many nations in the world (due to economic and logistical reasons), particularly in resource-poor nations. One of the key contributions of this study is that it offers cost-effective alternatives.
Title: New Challenges for Modelers of Infectious Diseases of Africa (with Emphasis on the Role of Discrete Mathematics and the DIMACS Initiatives)
This talk will discuss the background for the meeting and goals for it, with an introduction to the past and potential future roles of DIMACS. It will survey some of the main themes of the meeting: why model; special modeling challenges arising from African diseases; and issues raised by emerging diseases in resource-poor countries, from applying optimization methods to the use of scarce public health resources, from comparing alternative vaccination strategies, and from analyzing the connection between ecological change and disease. The talk will also describe topics in discrete mathematics that have not yet been widely used in mathematical epidemiology, including data mining, data cleaning, game theory, combinatorial group testing, and the theory of measurement.
Title: Optimize What? Issues in Optimizing Public Health Resources through Mathematical Modeling
The challenge in optimizing public health decisions, systems, and resources is that three concerns have to be addressed. First, an objective function has to be stated. This can be complicated when there are many factors to optimize and different stakeholders have different priorities. Second, constraints have to be specified Finally, results have to be presented and discussed. Results may be optimal for one segment of the population, but detrimental to others, presenting a significant challenge to public health officials. A decision tree model used to analyze the cost-effectiveness of Lyme disease vaccine illustrates these challenges. The model results showed that cost savings would occur if the vaccine was only used (i.e., targeted) in individuals whose annual risk of contracting disease was greater than 3%. In addition the model illustrated that an alternative technology, working to improve the likelihood of early detection and successful treatment was probably more cost-effective than vaccinating those with lower risk (e.g., 0.005/ year). A second example is a discrete-event computer simulation model that allocated staff in a vaccination clinic, with the goal of maximizing numbers vaccinated per day. The results indicated that clinic staff should focus on the groups with the largest numbers (i.e., the general population), which meant that special groups, like the frail and elderly, spend more than twice the time in the clinic as the other groups. Although alternative objective functions could have limited this disparity, it would have made the clinic less efficient, and thus not vaccinate the maximum number of people. These examples clearly illustrate the power of mathematical modeling to clarify a potential set of options and the consequences of those options. The results also clearly illustrate that mathematical optimization may run contrary to expectations.
Title: So Much to Model, So Little Time
This talk is an attempt to stimulate discussion on the prospects and opportunities for disease related modeling in the context of current epidemiological and physiological research in South Africa, especially as related to the HIV/AIDS problem. We outline a number of recent modeling applications that have come up in the local context in recent times. They range from low-level laboratory data analysis to epidemiological inferences. This diversity of mathematical applications, the relatively late stage at which modeling was introduced into these projects, and the small/transient group of modelers that has been involved, raises some tough questions about planning, prioritizing and managing research of this nature.
Title: Epidemics in Strongly Fluctuating Populations
We introduce an epidemic framework that includes both compensatory (contest competition) and overcompensatory (scramble competition) population dynamics with and without the Allee effect. We compute the basic reproductive number R0, and use it to predict the (uniform) persistence or extinction of the infective population, where the population dynamics are compensatory and the Allee effect is either present or absent. We also explore the relationship between the demographic equation and the epidemic process, where the total population dynamics are overcompensatory. In particular, we show that the demographic dynamics drive both the susceptible and infective dynamics. This framework is suitable for studying diseases in animal populations.