DIMACS Workshop on Facing the Challenge of Infectious Diseases in Africa: The Role of Mathematical Modeling

September 25 - 27, 2006
University of the Witwatersrand (Wits)
Sports Administration Building - the West Campus
Johannesburg, South Africa

Dominic Clemence, North Carolina AT&T State University, clemence@ncat.edu
Wayne Getz, UC Berkeley, getz@nature.berkeley.edu
Abba Gumel, University of Manitoba, gumelab@cc.umanitoba.ca
John Hargrove, SACEMA Director, jhargrove@sun.ac.za
Edward Lungu, University of Botswana, lunguem@noka.ub.bw
Fred Roberts, DIMACS, froberts@dimacs.rutgers.edu
Presented under the auspices of the Special Focus on Computational and Mathematical Epidemiology.

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:

Preliminary List of Confirmed Speakers:

Esimai Olapeju Adefunke, Obafemi Awolowo University

Title: Climate Modeling: A Stategy to Reduce Malaria Burden in Africa

Ecologists became interested in human infectious diseases because they provide rich dataset for testing mathematical models developed to understand the population dynamics of host-pathogen interactions. These models provide novel ways of examing the efficacy of public health interventions to control diseases which ultimately lead to insights into numerous ways in which vaccination and other intervention may be carried out. Malaria is life threatening parasitic disease in tropical regions transmitted by mosquitoes resulting in 300-500 million new cases and more than 1.5 million deaths every year (World Malaria Situation 1997). Majority of these deaths occur in children under age five and pregnant mothers. Malaria in particular is generally thought to be increasing because of climate change. Studies have suggested a linear relationship between global warming and malaria and that forecasting of climatic fluctuations which translate to forecasting of malaria outbreak assist in developing early public health interventions (population based surveillance, surface water control and insecticides treated nets) Mathematical models are required for the long ?range forecasting of changes in the potential transmission of malaria. The model will integrate units of time (months), units of surface area, the emission scenario ?based climate change process, mosquito and parasite system, and human population characteristics (size, age distribution and prior immunity). Climatic modelling therefore is an important consideration in the formulation of long-term priorities and policies in the control of malaria in Africa

Ayanna Alexander, Walter Simmons, George Mukira, and James Thairu, Asamoah Nkwanta, Morgan State University

Title: HIV-RNA Sequence Prediction: A Bioinformatics Classroom Experience

In this poster, the focus is placed on RNA sequence prediction using strands of HIV-RNA from the SL2 and SL3 structures. The amount of free energy released or absorbed by forming base pairs is used to quantify the stability of a secondary structure. Positive free energy refers to energy absorbed to form a configuration while negative free energy is that which is released. Therefore, the structure, which yields the highest negative free energy, is the structure which is most likely to be formed, because more stored energy is released. This poster illustrates how the combinatorics of RNA hairpins were applied to the respective sequences of the known structures of the SL2 and SL3 components of HIV-RNA, in order to reduce the minimum free energies of the sequences, thereby gaining better or more stable sequence predictions.

Mingxiang Chen, Dominic P. Clemence, and Gregory Gibson, North Carolina A & T State University

Title: Dynamical Properties of Some Finite Difference Schemes for an SI Epidemic Model

While extensively used for integrating dynamical population models, finite difference (FD) methods often suffer from step size-dependent instabilities. Using a two dimensional SI model from Hantavirus epidemics studies, some common instability problems with standard FD methods are highlighted. Numerical experiments and analysis are used to demonstrate how the RK-2 method can generate spurious equilibria, experience period-doubling bifurcations, and display chaotic behavior, as the step size varies. In contrast, simulation and analysis prove that some Nonstandard Finite Difference (NSFD) schemes for simulation of the model preserve the dynamical properties of that model.

Gerardo Chowell-Puente, Los Alamos National Laboratory

Title: Transmission and Control of Seasonal and Pandemic Influenza

Recurrent epidemics of influenza are observed seasonally around the world with considerable health and economic consequences. Major changes in the influenza virus composition through antigenic shifts can give rise to pandemics. The reproduction number provides a measure of the transmissibility of influenza. We estimated the reproduction number across influenza seasons in the United States, France, and Australia for the last 3 decades. In regards to pandemic influenza, we estimated the reproduction number for the first two epidemic waves during the 1918 influenza pandemic in Geneva, Switzerland. I will discuss the public health implications of our findings in terms of controlling regular influenza epidemics and an influenza pandemic of comparable magnitude to that of 1918.

Gerardo Chowell-Puente, Los Alamos National Laboratory

Title: Spatial Patterns of Infection: The 2001 Foot-and-Mouth Epidemic in Uruguay

I will present a county-based metapopulation model for the spread of foot-and-mouth disease (FMD). The model is validated against a null model based on the homogeneous mixing assumption by use of a spatial dataset of the 2001 FMD epidemic in Uruguay. The model is used to estimate relevant parameters and the role of interventions which included movement restrictions and a mass vaccination campaign.

Tanya D. Craft and Dominic P. Clemence, North Carolina Agricultural and Technical State University

Title: Analysis and Numerical Integration of a Mathematical Model of HIV Infection with HAART and a Putative Vaccine

We consider a pre existing model which looks at HIV Pathogenesis. Some of the model assumptions are: (1) one virus strain is present, (2) there is absence of within-host mutation, and (3) the only abnormality of the immune system is HIV infection. The model considers the interaction of five populations: naïve CD4+T cells, CD8+ T cells, actively infected CD4+T cells, latently infected CD4+T cells, and Virions. The difference between the two models is the assumption of the migration between actively and latently infected CD4+T cells; results of the comparison between the two models will be presented. Further, instabilities of standard integration methods for such models are explored using implementation in Stella. Nonstandard finite difference schemes, which are valid for all step sizes, are proposed to alleviate such method dependent stabilities.

Bassidy Dembele, Howard University

Title: Deterministic Method to Study the Spread of Malaria

We use deterministic method to study the spread of malaria disease in Mali. Two different situations are analyzed. First, we do our study with no seasonal effects on the vector populations. Next, we look at the seasonal influence on them. In Both cases, we show that the disease will die out when R0<1 than one whereas it will persist when R0>1.

Jesse Dill, Ailey Crow, Dennis Wylie, James Lloyd-Smith, Maria Sanchez, Judith Hahn, Kimberly Page-Shafer, and Wayne Getz, University of California

Title: Modeling Disease Transmission in a Heterogeneous Needle-Sharing Population

With the success of small-worlds network models and a new quantitative understanding of the disease "superspreader" phenomenon, the importance of population heterogeneity in epidemiology is growing increasingly clear. We describe a network model that implements a two-compartment population of injection drug users (IDU). The two compartments differ in their injection behavior; using real-world data from an urban IDU population, we discuss appropriate variables in which to introduce heterogeneity and their effects on disease transmission with application to the spread of Hepatitis C virus.

Nafiu Hussaini, Bayero University Kano

Title: Combatting HIV/AIDS in Some Rural Communities in Kano State, Nigeria: Practices, Challenges and the Role of Modeling

This poster reports on the impact of HIV/AIDS-related knowledge, attitudes, and behaviors on the risk of infection amongst sub-populations in some rural communities in Kano State, Nigeria. In addition to identifying some socio-cultural and religious factors that may influence the spread of HIV/AIDS in the communities, the study also outlines some of the difficulties associated with implementing anti-HIV interventions such as condom use. Suggestions for Africa-specific modelling, taking into account some peculiarities of African societies, would be made.

M. Ibrah1, O. A. Koita1, M. L. Touré2, M. Bouaré1, M. S. Maiga3, S. Traoré4, A. Diallo6, M. A. Barry5 and D. J. Krogstad7 ,
Laboratoire de Biologie Moléculaire Appliquée, Université de Bamako, Mali ; 2. Centre Régional d'Energie Solaire, Bamako, Mali ; 3. Faculté des Sciences et Techniques, Université de Bamako, Mali ; 4. Centre Médical Mère-Enfant, le Luxembourg, Bamako, Mali ; 5. Programme d'appui à la lutte contre le SIDA du CDC, Bamako, Mali ; 6. Faculté de Médecine, de Pharmacie et d'OdontoStomatologie, Universite de Bamako, Mali ; 7.Tulane University, New Orleans, USA.

Title: Solar UV-B Radiation and Malaria in Mali

In this study, we examined the relation between malaria and solar UV-B. In particular, we estimated the monthly variations of solar UV-B and compare its intensity with malaria cases in Bamako (Mali). We observed high values of UV-B in September of 2000 and March of 2001. Exactly one month later, we observed a large peak of morbidity in October 2000 and a small peak in April 2001. Radiations were correlated with rainfall and temperature (Pearson Correlation=-0.631; p=0.028 and Pearson correlation= 0.681; p=0.015 respectively). However, we did not demonstrate a conclusive significant relation between solar UV-B and malaria (Pearson Correlation= -0.529 and p=0.077). Clouds were more frequent in Bamako during the winter and could attenuate the strong intensities of UV-B radiations observed between September and October 2000. These results indicate a month lag between the peaks of malaria morbidity and the intensity of solar UV-B in Bamako. In human host, residual parasitemia could be impacted by UV-B. This induces disease progression in period of the year when malaria transmission does not occur.

Moatlhodi Kgosimore, Botswana College of Agriculture

Title: Vertical Transmission of HIV/AIDS Model with Density Dependent Demographics

The asymptotic behaviour of solutions of infections disease transmission models depends not only on the epidemiological formulation, but also on the demographic process incorporated in the model. The effect of vertical transmission is usually ignored in most HIV/AIDS transmission models even though it has a significant bearing in changes in population demographics. We account for vertical transmission of HIV/AIDS in a population and study its effects in the dynamics of the disease. We derive conditions under which the disease is likely to die or spread in a population. Numerical simulations are carried out to demonstrate some of the demographic factors that influence the dynamics of the disease in a population.

Justin Lessler, Johns Hopkins Bloomberg School of Public Health

Title: A Computational Model of Evolvable Viruses in Populations, System and Applications

The constant evolution of viruses is an important aspect of some of the most important challenges in the control of infectious disease. The emergence of novel viruses, drug resistance and risks associated in using live attenuated vaccines are all areas where the evolution of viruses is a driving force. We developed a computational simulation of evolving viruses in populations in order to better understand these phenomena.

In this poster we present the key elements of this system and illustrations of its application to two key public health challenges in Africa, and the world at large. The first is the problem that epidemics of circulating vaccine derived polio virus pose to the global campaign to eradicate polio. We use our system to examine the relationship between vaccine coverage and the occurrence of these epidemics. The second application is the emergence of novel viruses from cross species transmission. We examine how different evolutionary strategies and the presence of "transitional species" effect the frequency with which viruses jump the species boundary.

Angelina Lutambi, Wits

Title: Delayed Death in HIV Spread Models

HIV patients in Africa are known to survive for around 10 years before dying of AIDS. The survival time is expected to have an impact in the spread of the disease. We use mathematical models to understand the effect of different survival patterns. A model that considers an exponential distribution of AIDS mortality is extended to include a delay in the occurrence of death. It is found that during the early stage of the epidemic, both incidence and prevalence curves are very similar in both models. However large differences occurs during the mature stage of the epidemic. Within the model with delay, different delay times give similar rise in the incidence and prevalence curves at low t. Furthermore, in the model without delay, the effect of changing the survival time is shown right from the beginning of the epidemic. Periodic solutions also develop in the model with delay as some of the parameters are changed to values which are however not physical. Clearly, the time series curves for the mortality rate are distinctly different in the two models. The findings suggest that the inclusion of a delay in the infectous peroid for the HIV spread models is an important factor since it may affect the estimates

David Murillo, ASU

Title: Change in Host Behavior and its Impact on the Co-evolution of Dengue

The joint evolutionary dynamics of dengue strains are poorly understood despite its high prevalence around the world. Two dengue strains are put in competition in a population where behavioral changes can affect the probability of infection. The destabilizing dynamic effect of even "minor" behavioral changes are discussed and their role in dengue control is explained

Eustasius Musenge, University of Witwatersrand

Title: Modelling Anti-TB Drug Induced Hepatotoxicity

Anti-TB drugs cause liver damage. The liver is one of the largest and most important organs in the human body. It carries out many vital functions, such as decomposing toxins within the human blood stream into products that can be readily removed through bile or urine. Damage to a liver occurs when toxins are accumulated faster than the speed of detoxication, thus resulting in hepatotoxicity, which is liver damage caused by medications and/or chemicals, also known as Drugs Induced Hepatotoxicicty (DIH). HIV positive patients and those taking several drug regimes are at the most risk of developing DIH.

Hepatotoxicity is a common problem in drug treatment trials but is observed only indirectly through biomarkers measured in the blood. This creates the need to infer an individual's unobserved liver function dynamically using blood tests and other patient baseline characteristics. Some of the challenges with data collected are high dimensionality, irregular time observation points over patients, missing observations, and noise involved in measurement and biological processes.

The current assessment of hepatic injury caused by a drug is usually based on circumstantial evidence. This also depends on suspicion by the clinician who recognizes that the time of onset of liver injury may be related to the introduction of a therapeutic agent, and thus is often inaccurate. This research aims at modeling hepatic injury in a way that may assist in its early detection and thus minimize on cost , timely introduction of intervention methods and reduce adverse events.

Gasper Godsong Mwanga, Wits

Title: Estimating HIV Incidence from Prevalence of "Recent Infection"

We review and critique methods for estimating incidence from the prevalence of a category of "Recent Infection", defined by the use of two thresholds, as measured by possibly different laboratory assays, reached at different times following HIV infection. The periods patients spend between these thresholds, called a "window period", differ from patient to patient, and from study to study. The estimation of this window period is problematic. Using patient follow-up data from the acute infection cohort of the Centre for the AIDS programme of research in South Africa (CAPRISA), we systematically infer the mean window period duration, in a distribution (shape) independent way (3 - 13 days, 95% CI). We independently infer the incidence rate (5% - 11%, 95% CI) and the prevalence of the window period state (0.06% - 0.34%, 95% CI) from the same data set, noting consistency between these three inferred parameters. We discuss the use of mathematical models of acute HIV-1 infection, for adapting the inferred window period duration to a different study, such as a single snapshot of the prevalence of the window period state, where the window period is not directly observed and the assays used may have different detection thresholds.

Farai Nyabadza and Edward Lungu, University of Botswana

Title: Modelling the Role of Chemoprevention in Malaria Control: the Case of Southern Africa

Malaria is by far the world's most persistent tropical parasitic disease and is endemic to tropical areas where the climatic and weather conditions allow con- tinuous breeding of the mosquito. A model for the transmission of malaria with chemoprevention is analyzed. The stability analysis of the equilibria is presented with the aim of finding threshold conditions under which malaria clears or persists in the human population. Our results suggest that eradication of mosquitoes and chemoprevention can significantly reduce the malaria burden.

Omayra Ortega, Arizona State University

Title: Cost-Benefit Analysis of a Rotavirus Immunization Program in the Arab Republic of Egypt

Rotavirus diarrhea is a significant cause of morbidity and mortality in Egyptian children aged 0-5 years. In light of recent developments in rotavirus vaccine development and licensing, one contributing factor to assist decision and policy makers on whether to add rotavirus vaccination to national immunization programs is to understand the costs and benefits from such type of policy decision. In Egypt, approximately 1,909,000 children are born each year. Within this birth cohort of children, 3000 die before they reach the age of five, while close to 1,813,550 will have become ill with rotavirus by the age of five. The Egyptian Ministry of Health and Population (MoHP) is the main payer of health care and responsible for administering the Expanded Program on Immunization with the country. To inform these decision makers, a cost- benefit analysis, from the perspective of the MoHP, based on available local data from published and unpublished sources was conducted to evaluate the economic impact of introducing a rotavirus vaccine to the current national immunization schedule.

Rachid Ouifki and Gareth Witten, SACEMA

Title: Model of HIV-1 Life-Cycle with Periodic Drug Efficacy and Three Intra-Cellular Delays

We present a model of HIV-1 infection with three intracellular delays and periodic HAART treatment with interruptions. We showed numerically that the model exhibits oscillations and examined analytically the stability of the viral free and the infected steady states. Based on the stability results, we derived an effective strategy for reducing the viral load.

Cissé Ousmane, Koita Ousmane, University of Bamako, James Colborn, Krogstad Donald, Tulane University and J. Ylostälo, Center for Gene Therapy

Title: Gene Expression Analysis in Human Uncomplicated Plasmodium Falciparum Malaria

Malaria is a major public-health problem in developing countries. Activation and modulation of the human immune response are critical in evolution of the disease. High-density oligonucleotide microarrays make it possible to examine the mRNA transcripts for most genes simultaneously in a way that has not been possible previously. The application of microarrays was used previously in monkey models with malaria infection. However, the interpretation of human microarray data is frequently compromised by the variability of the results, by limitations in study design and inter-individual variation based on genomic DNA. To explore gene expression, we took 3 serial blood samples from children with uncomplicated Plasmodium falciparum malaria. We used these samples for RNA isolation. Isolated RNA was then used to study gene expression with Affymetrix GeneChip analysis. The first sample is taken at the time of the patient's initial presentation with positive thick smear, positive P. falciparum antigen test, and malarial clinical symptoms). The second sample is taken 3 days later (after 3 days of antimalarial treatment). The third is taken after finishing 3 days of oral treatment (10 days after presentation) when the patient has recovered and becoming asymptomatic. Inter-individual differences were controlled by using three samples from the same individual. Uninfected children (controls) were treated in the same conditions as infected children to examine the effect of anti-malarial drugs on human gene expression. Confounding by changes in baseline gene expression was addressed by using the expression of cytoskeletal and cytoskeleton genes (Gene Ontology classification) as internal controls. Using this strategy, 10 subjects with uncomplicated malaria were enrolled for the study. Data from 30 samples were filtered and clustering in dChip and the pathways were analyzed using GenMAPP 2.0. Microarray data were validated by immune profiling low density arrays. Malaria produced significant increases in the expression of genes in the GO classifications for defense, immune response, response to external stimuli, response to pathogen or parasite, innate immune response, and response to stress (P = 10-6 to 3x 10-6). In contrast, there were no significant changes in expression of genes in the cytoskeleton organization/biogenesis GO classifications (P = 0.38 and 0.62) and also only one gene was found with a significant change for uninfected controls. Differential expression profiles have been identified in all the patients. Analysis of gene network and pathways involved in uncomplicated P. falciparum infection showed that genes in cytokine and inflammatory response and apoptosis pathways were strongly correlated with the disease severity and level of parasitemia. These results demonstrate the value of microarrays for studying the response of the human transcriptome to malaria infection and provide a new prognostic marker.

Carel Pretorius, SACEMA

Title: Investigating Viral Parameter Dependence on Cell and Viral Life Cycle Assumptions

We review population dynamic type models of viral infection and introduce some new models to describe strain competition and the infected cell lifecycle. RT-PCR data from a recent clinical trial, tracking drug resistant virus in patients given a short course of monotherapy is comprehensively analysed, paying particular attention to reproducibility. This analysis demonstrates the subtlety associated with quantifying and interpreting viral load fractions. A Bayesian framework is introduced, which facilitates the inference of model parameters from the clinical data. It appears that the rapid emergence of resistance is a challenge to popular unstructured models of viral infection, and this challenge is partly addressed. In particular, it appears that minimal ordinary differential equations, with their implicit exponential lifetime (constant hazard) distributions in all compartments, lack the short transient timescales observed clinically.

Nicole Ramsey, Howard University and Minority Health Disparities International Research Training Program, Moussa B M Cisse, Boubacar Diallo, and Ousmane Koita, Laboratory of Applied Molecular Biology, University of Bamako

Title: Correlation of the Prevalence of Hemoglobin S, Anemia, and Plasmodium Falciparum Malarial Infection among Children in the Village Sirakoroba of Kolokani, Mali

Anemia is a common blood disorder due to a low presence of red blood cells in the body. In sub-saharan Africa, anemia is a multi-factorial disease, where poor nutritional status, intestinal helminthes, HIV infection and hemoglobinopathies are the main factors. Malaria is one cause of hemolytic anemia and genetic disorders such as sickle cell anemia, are also involved in anemia. This poster will present the results of a study that examined the role of hemoglobin AS in induction of anemia among children between 1 and 10 years of age in the malaria-endemic village Sirakoroba.

Karyn Sutton, and Carlos Castillo-Chavez, Arizona State University

Title: Models of Pneumonia and their Implications for Developing Countries

Although pneumonia has long been the subject of study in the biological community, this disease remains a significant cause of morbidity and mortality. Pnuemonia, commonly a secondary infection of influenza, is a leading cause of death worldwide following a bout with an infectious disease. We have developed mathematical models of these processes in an effort to understand the mechanisms responsible for their persistence. We are able to show that the spread of pneumonia as a result of contacts are insignificant in a realistic parameter regime. Thus, the successful establishment of a pneumonia infection is determined primarily by the hosts immunological and nutritional status. Further, we show that while incidence can be significantly reduced with improved nutrition, it is likely to remain high when nutrition is poor. Thus, regions with a large proportion of disadvantaged persons will continue to be affected without assistance.

Tinevimbo Shiri, National University of Science and Technology

Title: HIV Strain Dynamics: Continuous Optimal Therapy

We explore a two - strain HIV dynamic mathematical model with symmetric mutation channels to simulate the effect of continuous highly active antiretroviral therapy (HAART) on an individual who has been infected for a long time. We derive continuous optimal therapeutic strategies by formulating and analyzing an optimal control problem. We show simulation results which ensure over a variety of conditions using a standard numerical technique based on Pontryagin's Maximum Principle.

Evelyn Thomas, Howard University

Title: The Effect of HIV on the Spread of Gonorrhea Among Black Women in the US, Caribbean, and Brazil

The HIV epidemic has taken its toll globally; it is estimated that 17.3 million women around the world are currently living with the virus. In the US alone, African American women make up a disproportionate amount of new HIV cases. It follows that other female populations, namely descendants of the Trans-Atlantic slave trade, are affected as well. Consequently, the prevalence of this virus serves as a vehicle for the spread of other sexually transmitted diseases. The CDC suggests that the environment provided by nonulcerative STDs such as gonorrhea (one of the most common sexually transmitted diseases) facilitates high HIV coinfection rates. In this introductory analysis of epidemic modeling, a model is created and examined that describes the role HIV plays on the spread of gonorrhea by incorporating the existence of symptoms of gonorrhea and knowledge of HIV status.

Daniel Westreich and Annelies Van Rie, UNC-Chapel Hill

Title: How to Target TOPS: Combivir to Reduce Nevirapine-Resistance after PMTCT. A Stochastic Model

Background: Single dose nevirapine (sdNVP) has proven highly effective at preventing mother-to-child transmission (PMTCT) of HIV in low-resource settings. Unfortunately, sdNVP-based PMTCT frequently results in NVP-resistance, which may lead in turn to faster virologic failure of highly active antiretroviral therapy (HAART). Investigators have dramatically reduced prevalence of NVP-resistance in women receiving sdNVP by adding a 7-day short-course of Combivir (AZT + 3TC) after sdNVP (the "TOPS" protocol). In resource-limited settings, it may be important to understand which women will benefit most from TOPS.

Methods: We performed stochastic simulations of 10 years of follow-up in cohorts of 10000 pregnant, HIV+ women in sub-Saharan Africa. We modeled impact of TOPS by comparing mortality in women receiving sdNVP alone to mortality in women receiving sdNVP plus TOPS, assuming that HAART would become available for eligible women (CD4 < 200) between 0 and 5 years after PMTCT. We determined results by CD4-strata (0-200, 200-350, 350-500, 500-800, 800-1100). Model parameters were based on published and unpublished data, preferentially from African populations.

Results: Simulations predict that at five years post-PMTCT, the TOPS-attributable reduction in mortality is largest among women with CD4 counts of 200-350 during pregnancy, when HAART becomes available within four years of PMTCT. Ten years post-PMTCT, the impact of TOPS is maximized among women with CD4 counts of 200-350 when HAART becomes available within three years. When HAART becomes available four or five years post-PMTCT, the ten-year impact of TOPS is as large or larger among women with CD4 counts of 350-500 as in women with CD4 counts of 200-350.

Conclusions: Our model suggests that when there is insufficient Combivir for universal TOPS among pregnant women not receiving HAART, the impact of TOPS may be maximized by careful selection of a CD4-stratum-specific subpopulations for the intervention, a selection which should be informed by any projected delay in HAART availability.

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Document last modified on September 15, 2006.