HIV

Understanding how the HIV-1 virus actively diminishes the immune system's capability of response, and HIV-1's ability to mutate, which ultimately leads to drug therapy failure, are arguably some of the most important medical problems of the 21$^{st}$ century. In fact, while researchers worldwide are actively combating this disease, we still lack an understanding of many of the fundamental properties of its pathogenesis. I propose to develop and analyze several mathematical models that account for many stages of the HIV-1 infection process. Such an effort will be the first of its kind combining theory and experiment to map the infection process from primary infection, through the period of latency, to drug therapy and the emergence of drug resistance. The proposal is experimentally driven in that we will continue to fit the models, using statistics and analysis, to patient data from Dr.~David D. Ho's laboratory at Aaron Diamond Aids Research Center, to acquire more information about the infection process. Also, the proposal is mathematically important in that we have included time delays which are necessary in any model of a cellular process and through a detailed mathematical analysis we will be able to highlight the dominant features of the infection process that are not seen solely through statistics or computation.

Our mathematical models of the dynamics of HIV-1 infection after the initiation of drug therapy have already assisted in determining many quantitative features of the interaction between HIV-1 and the corresponding immune response. Our results have provided quantitative support to several new hypotheses about the disease. Our research has focused on the use of models which account for intracellular delays in the infection process and have shown that this more accurate representation of the cell biology substantially changes the estimates of the death rate of productively infected T cells, $\delta$, and the viral clearance rate, $c$. We have shown that the previously reported values for $\delta$ were underestimated by nearly $23 \%$ and then showed quantitatively how the average life span of infected T cells is partitioned between infected but not producing virus and productively infected. Also, we have shown that the levels of drug effectiveness in patients on antiviral therapy can be as low as $70 \%$, which implies the need of better drug therapies. Based on the success of our preliminary research, I now am working to modify and extend the models to investigate more complex issues. The specific aims of my research is to answer the following questions.

1) What can we learn about HIV-1 and immune system's dynamics through the analysis of these delay differential equation models and can we present this mathematical theory in a way that researchers, studying HIV-1, hepatitis C and hepatitis B, will be able to use?

2) How will changing the models by accounting for age dynamics, i.e., the age of an infected cell, affect parameter estimates?

3) Can we predict and prevent the imminent failure of drug treatment due to viral mutation?

4) What are the causative agents involved in the gradual decline of \CD4 T cells, the main target cell of HIV-1, which eventually leads to AIDS?

5) What is the best way to incorporate sensitivity analyses, model indentification and statistic analysis into our models?

Return to Home