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Summer 2007
Dynamics of Targeted Treatment
Issac J. Michaud, University of Maine
Samuel F. Potter, University of Arizona
David Murillo, Arizona State Univeristy
David E. Hiebeler, University of Maine
Young S. Lee, Manchester College
Tae S. Do, Kwandong University
Faina Berezovskaya, Howard University
MTBI-04-01M
Abstract: An SIS
epidemiological household model is studied to understand the
dynamics of targeted treatment. The household model splits the
population into households, which may, for example, represent
patches within a landscape or dorms within a school.
Interactions between households typically occur at a much lower
rate than intra-household interactions. In an agricultural
setting, households are crop fields that can be infected with
insect pests. Plants will recover when insecticide is applied
and the insects on them are killed. Rather than using a fixed
per-capita recovery or treatment rate, an individual's treatment
rate will be a function of the infection level in that
individual's household. This allows for targeted treatment
directed towards households with larger infections. A model is
developed and a moment-closure approximation approach is used to
truncate the resulting infinite system of differential
equations. Numerical results from the truncated system are
computed and compared to stochastic simulations. It was found
that targeted treatment does not change the endemic equilibrium
when the population-wide treatment rate is controlled.
Surprisingly, targeted treatment decreases the amount of time it
takes to reach the steady state, which could be detrimental
during an epidemic.
The Effects of Cycling on Drug Resistance HIV
Aaron Abromowitz, Harvey Mudd College
Andre Robinson, Medgar Evers College CUNY
Walter Chambliss, Alabama State University
Emmanuel J. Morales-Butler, Universidad Metropolitana
Anuj Mubayi, Arizona State University
Xiaohong Wang, Arizona State University
Abdessemad Tridane, Arizona State University
MTBI-04-02M
Abstract: Zidovudine and Didanosine are administered in cycles as a part of an HIV drug therapy. Both are Reverse Transcriptase Inhibitors (RTIs) that is, they inhibit the replication of the virus in the infected CD4+ T- cells. A mathematical model is formulated that incorporates four types of viruses: wild, resistant to Zidovudine, resistant to Didanosine and resistant to both. The lower bounds for drug efficacies are found by calculating the basic reproductive number assuming constant efficacies. A systematic study of drug therapy schemes via numerical simulations with emphasis on the dynamics of viral count as a function of drug resistance is performed. The results show that although there is no optimal schedule for switching of drugs, it is generally better to switch them within shorter time periods.
A Cost Analysis of Human Papillomavirus: Individual Education vs. Mass-Media Campaign
Alison Green, Canisius College
Yeni Nieves, Purdue University
Cindy Enrigue, University of California
Dori Luli, Arizona State University
Britnee Crawford, University of Texas at Arlington
Christopher Kribs-Zaleta, University of Texas at Arlington
MTBI-04-03M
Abstract: Human Papillomavirus (HPV), a common sexually transmitted virus, is a collection of more than 100 viruses, some of which (called "high-risk" oncogenic or carcinogenic HPV) are associated with certain types of cancer. HPV 16 and 18 cause approximately 70% of all cervical cancer. An estimated 11,150 new cases of cervical cancer will develop in the U.S. in 2007. In 2006, the FDA approved the first vaccine to prevent cervical cancer, designated for females aged 9-26, called Gardasil. Studies have indicated Gardasil has a 95-100% success against HPV types 6, 11, 16 and 18. Many studies have shown that there exists a lack of HPV awareness, as well as knowledge of causes, effects and preventive measures. In this study we compare two strategies for controlling the spread of carcinogenic HPV in the population, while minimizing cost. The research is conducted via a cost analysis of a mandatory vaccination policy vs. a mass-media awareness campaign, each individually modeled with a system of differential equations. Mandatory (but not universal) vaccination includes individual-based education at the time of vaccination only, while the mass-media campaign is assumed to be ongoing. In both cases the education influences females to get vaccinated and/or reduce their sexual activity, but is of limited duration. We use qualitative analysis to derive the respective control reproductive numbers, and numerical analysis to obtain the total costs of vaccination, education, high sexual activity, and expected cancer treatment costs for infected females in both models. Our results support the conclusions of a 2005 study analyzing the epidemiology of HPV with a potential vaccination that even in the presence of a vaccine, the infective population will remain large due to a high transmission rate. Our results also support the conclusion that a high transmission rate and a high reproductive rate require a high efficacy and high vaccine coverage to eliminate the epidemic.
Romarie Morales, University of Puerto Rico
Helene Nehrebecki, Arizona State University
Carolina Pontones-Argueta, Instituto Tecnologico Autonomo de Mexico
Jose M. Vega-Guzman, Arizona State University
Anuj Mubayi, Arizona State University
Joaquin Rivera, Arizona State University
MTBI-04-04M
Abstract: In recent years, communicable diseases, such as The Avian Flu and SARS, have dominated the news, and in the process, they have had tremendous impact on public health policies. In this paper, we introduce a mathematical model that is used to study the epidemics and pandemics. The work is motivated by data on the 1918-1919 influenza pandemic in the cities of Montreal, Canada and Winniped, Canada. We estimated model parameters for the two cities using 1918 fall were epidemic data using least square fitting. We then explore the role of heterogeneity via a two-patch (city) model. For the single-patch model, we derive a formula for a final size epidemic and the basic reproduction number (R0). R0 is found to be 14.58 for Montreal and 5.39 for Winnipeg. The number of asymptomatic cases in Montreal and Winnipeg were found to be approximately 200,000 and 60,000, respectively. We surmise that the low reporting and high number of asymptomatic cases can be explained by a lack of public health facilities, and higher severity of the disease during that period.
Karen C. Chow, Arizona State University
Xiaohong Wang, Arizona State University
Carlos Castillo-Chavez, Arizona State University
MTBI-04-05M
Abstract: Hospital-acquired infections caused by antibiotic-resistant bacteria pose a significant threat to public health. Antimicrobial cycling, in which antibiotic classes are alternated over time, has previously been suggested as a strategy for curbing the development of resistance in hospitals. A mathematical model of antimicrobial cycling in a hospital setting is developed in order to analyze the efficacy of such a program, with an emphasis on the emergence and significance of dual resistance. Simulation results compare the effects over time of antimicrobial cycling programs with mixing programs and their ability to reduce antimicrobial resistance. Our model also considers the effects of isolating patients harboring dual-resistant bacteria in the hospital.
A mathematical model of HIV and Malaria Co-Infection in Sub-Saharan Africa
Kamal Barley, Arizona State University
Sharquetta Tatum, Alabama A & M University
David Murillo, Arizona State University
Svetlana Roudenko, Arizona State University
Ana M. Tameru, Alabama State University
MTBI-04-06M
Abstract: Malaria and HIV are two of the most deadly diseases in Africa. Combined they account for 4 million deaths each year, and according to the Center for Disease Control and Prevention (CDC), there is an estimated 5 percent increase in malaria deaths due to HIV infection in Sub-Saharan Africa. Since the co-infections was recorded, malaria has seen a 28 percent increase in its prevalence. Malaria associated death rates have nearly doubled for those with co-infections. We introduce a system of differential equations linking the host-vector system of malaria with co-infection with HIV. We use data from Sub-Saharan Africa in general and Malawi in particular where co-infections from both disease in order to motivate and guide the behavior of our model. We discovered that when parameter ρ is alter it will effect the way the diseases interact with each other as well as separately.
A Dynamical Interpretation of the Three-Strikes Law
Susan Seal, Arizona State University
William Z. Rayfield, University of Maryland Baltimore County
Carl Ballard II, Alabama State University
Holden Tran, Northwestern University
Christopher Kribs-Zaleta, University of Texas at Arlington
Edgar Díaz, Arizona State University
MTBI-04-07M
Abstract: California's Three Strikes Law
has been in effect since 1994. Advocates of this policy claim it
acts as a deterrent for violent crime; yet critics allege it
acts solely as an incapacitant-a device used to segregate a
population of "undesirables" from the total population in an
attempt to lower criminal susceptibility. To determine the true
relationship between these two intimately connected phenomena,
we construct a dynamical model of the Three-Strikes Law within
the framework of inner-city communities located in Los Angeles
County. We then compare this model to one of Los Angeles County
before California implemented the Three-Strike policy-the
classical incarceration model. Through qualitative analysis we
determine the basic reproductive number, R0, for each of the
models. Using numerical simulations, we then determine the net
change in the total population of reformed inmates and the total
number of incarcerated individuals due to the Three-Strikes Law.
We also analyze the impact of population density on crime rates
in states that utilize the Three-Strikes Law. Finally, we
construct and examine a hypothetical One-Strike model to
determine the impact of different strike policies on the
reformed, criminal and incarcerated populations. We find that
the Three-Strikes policy deters crime better than the classical
incarceration policy in densely populated areas like Los Angeles
County. In the context of population density, the Three-Strikes
Law is a better deterrent in a sparsely populated region than a
densely populated region. The optimal policy is found to be one
that consists of more than three strikes.
The Cursed Duet: Dynamics of HIV-TB Co-infection in South Africa
Diego Chowell-Puente, Facultad de Ciencias
Brenda Jimenez-González, Instituto Tecnolígico Autonomo de Mexico
Adrian Nicholas Smith, University of Washington
Karen Riíos-Soto, University of Washington
Baojun Song, Cornell University
MTBI-04-08M
Poster sessions award recipient at the National 2007 SACNAS convention in Kansas City, MO
Abstract: In South Africa there is an increasing public health concern for the HIV/AIDS pandemic coupled with high tuberculosis (TB) prevalence. The progression of these infectious diseases compliments each other to produce a deadly synergistic effect. This results in devastating morbidity and mortality in communities suffering from HIV/AIDS-TB co-infection. HIV/AIDS-TB spells economic disaster for developing countries, nearly 30% of the annual household income. We use a epidemiological model to explore the co-infection transmission dynamics of HIV/AIDS and tuberculosis in South Africa, specifically in adults aged 15-49. We analyze our model to gauge the extent to which the HIV/AIDS epidemic accentuates the TB epidemic. Will the TB epidemic persist without the presence or prevalence of the HIV/AIDS epidemic? Our parameter values are estimated from demographic data. Sensitivity and uncertainty analysis are employed to determine the parameter value(s) to which the basic reproductive number is most sensitive. We run numerical simulations to predict future trends of both the HIV/AIDS and TB epidemics.
Modeling B cell Dysfunction in HIV infection
Loan Nguyen, Arizona State University
Tagan Griffin, Arizona State University
Abdessamad Tridane, Arizona State University
Yang Kuang, Arizona State University
MTBI-04-09M
Abstract: Progression from infection with the Human Immunodeficiency Virus (HIV) to AIDS is a complex process that remains poorly understood. While mathematical models representing the ongoing battle between HIV and the immune system have been successful, they remain focused on cellular, as opposed to humoral, immunity. This situation remains in spite of the fact that recent evidence has shown the mediators of humoral immunity, the B cells, to represent a significant factor in the progression to AIDS. We propose here a mathematical model of HIV infection, which, in addition to B cells, includes a population of so-called "dysfunctional B cells." These cells are improperly activated by HIV and contribute towards the progression to AIDS as they waste valuable immune resources and promote autoimmunity, which often accompanies HIV infection. By including more relevant aspects of the immune system into our model, we intend to suggest useful experiments as well as gain a more comprehensive picture of HIV infection.
A Model of the Drosphila Heart
Odalys Colon-Rentas, Arizona State University
Irina Kareva, University of Maryland
Pamela Reitsma, University of Maine
Genevieve Toutain, Arizona State University
Sharon Cook, Arizona State University
MTBI-04-10M
Mathematics talk award recipient at the National 2007 SACNAS convention in Kansas City, MO
Abstract: The heart of Drosophila melanogaster is a tubular organ that contains two types of excitable cells which work together to pump hemolymph through the body. At the cellular level, specific ion channels involved in the heartbeat of Drosophila have been identified and studied using genetic mutations and pharmacological agents. In this work the Drosophila heart is modeled as a network of excitable cells in order to explore the biophysical mechanisms underlying the generation of the heartbeat. The model cells are arranged in a tubular shape to form a network connected by gap junctions. Pacemaker cells with an intrinsic rhythm are added at one end of the network model and generate a wave of contraction down the heart. Using the model, channel kinetics are manipulated to explore the effects of different channels on Drosophila heartbeat. Model results are compared to experimental data.
Cats Protecting Birds Revisited with a Spatial Approach
James Gambino, Columbia University
Marco V. Martinez-Martinez, Universidad Javeriana
Kehinde Salau, Arizona State University
Edme L. Soho, Montclair State University
David E. Hiebeler, University of Maine
Fabio Sanchez, Cornell University
David Murillo, Arizona State University
MTBI-04-11M
Abstract: The mesopredator release hypothesis (MRH) suggests that in the absence of large, dominant predators, a population of smaller predators increases and, in the process, generates a decline in the prey community. The MRH has been used in attempts to comprehend problems involving the management of introduced species in islands and the extinction or declination of super predators in an ecosystem due to anthropogenic pressures. The dynamics of this system were studied using a spatially explicit model with mean field and pair approximations. We included mathematical analysis of the mean field model as well as numerical analysis for both approximations. The results of the simulation support the claims of the MRH and suggest that control of the mesopredator population is the most feasible method to ensure the persistence of endangered prey populations. Spatial modeling is a complex but valuable tool for studying such phenomena occurring in nature.