Disease Modeling Commons^™

Modeling The Effect Of Human Behavior On Disease Transmission, Katie Yan

Rose-Hulman Undergraduate Mathematics Journal

Many infectious disease models build upon the classic Susceptible-Infected-Recovered (SIR) model, a compartmental system that is used to simulate disease transmission in a population. The SIR model focuses on the transmission of disease but rarely includes behavioral or informational components that explore how disease perception influences transmission. In this paper, we propose a six-compartment behavioral SIR model that further segments the classic SIR system based on knowledge of information about the disease, and we explore how sharing information affects disease transmission. We designate two states as aware and unaware based on whether the relevant information is known by the population. …

Mathematical Modeling Of Type 1 Diabetes, Gianna Wu

HMC Senior Theses

Type 1 Diabetes (T1D) is an autoimmune disease where the pancreas produces little to no insulin, which is a hormone that regulates blood glucose levels. This happens because the immune system attacks (and kills) the beta cells of the pancreas, which are responsible for insulin production. Higher levels of glucose in the blood could have very negative, long term effects such as organ damage and blindness.

To date, T1D does not have a defined cause nor cure, and research for this disease is slow and difficult due to the invasive nature of T1D experimentation. Mathematical modeling provides an alternative approach …

Mathematical Aids Epidemic Model: Preferential Anti-Retroviral Therapy Distribution In Resource Constrained Countries, Nadia Abuelezam

HMC Senior Theses

HIV/AIDS is one of the largest health problems the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. ART-distribution methods need to be created that prevent the largest number of future HIV infections. We have developed a compartment model that tracks the spread of HIV in multiple two-sex populations over time in the presence of limited treatment. The model has been fit to represent the HIV epidemic in rural and urban areas in Uganda. With the model we examine the spread of HIV among urban and …

Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore

All HMC Faculty Publications and Research

In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing …

Aids: Prophecy And Present Reality, Victor De Gruttola, William Ira Bennett

New England Journal of Public Policy

Mathematical modeling of the AIDS epidemic can be useful for policymakers even though precise projections are not possible at this time. Models are useful in establishing ranges for current and future prevalence of HIV infection and incidence of AIDS, as well as in predicting the effect of a given intervention strategy. Most decision makers are using models implicitly when they use epidemiological information as a basis for policy; formulating a model explicitly permits examination of the underlying assumptions. By creating and testing a variety of models, an investigator can determine whether the models reflect more the underlying assumptions or the …