Tuberculosis lives in about 2 billion individuals but primarily in an inactive state. The emergence of HIV and malnutrition and famine in various parts of the world increases the likelihood that large number of individuals will develop an active form of the disease. What would be the consequences of TB re-emergence? I will discuss some potential outcomes that would add to the global health issues that we face today.
The volume of data available from the human genome and the genomes of other species leads to the need for research in the assimilation and analysis of very large data sets. This analysis is largely statistical, but cannot be carried out by statisticians alone - a meaningless analysis will likely result if not carried out in conjunction with a biologist. Ideally, what is now needed, and will be needed even more in the future, is a new type of scientist who is trained in computational, statistical and biological fields. Clearly the training of such people presents challenges. These challenges will be described, and the research opportunities that are available for researchers trained in this way will be discussed.
At the restriction point of its first growth phase G1, the cell must decide whether to go into the S phase, apoptosis, or the quiescent phase G0. A similar decision is made just before the cell is ready to go into mitosis. The above decisions are affected by the cell's environmental conditions, e.g., hypoxic neighborhood, overpopulation, etc. When some genes are mutated, the decision to go into S may be made in spite of unfavorable conditions, such hypoxic conditions, and this leads to tumor proliferation.
The multiscale model we shall discuss deals with the effects of gene mutation during the time a cell spends in each phase, as well as during the absolute time. After formulating the general model, I shall deal with much simpler situations whereby the cells are divided into only three different populations: proliferating, quiescent, and dead cells. In the even simpler case when we have only proliferating cells, I shall describe mathematical results such as global existence and bifurcation for PDE free boundary problems. It will be very challenging to extend these results to models which include several classes of cells.
First the bad news: the world's population changed from 1.7 to 6 billion during the 20th Century, forests are now cut down at an ever increasing rate, global warming is a fact, new diseases-such as West Nile virus, Rift Valley fever, hanta virus and XDR (extensively drug resistant) tuberculosis-are emerging, species are being lost at an incalculable rate, and heavy metals are polluting our food chain. Now the good news: these problems have created an urgent demand for mathematical ecologists. Most people think of mathematicians as nerds. However, applying mathematics to ecological, resource management, conservation biology, and epidemiological problems provides great opportunity for travel, being outdoors, and feeling useful to boot. In this presentation, I will illustrate these various opportunities from my own work and that of my students. Among other things, I will discuss: the role wolves play in Yellowstone in mitigating the effects of global warming, the structure of elephant societies and their conservation in the Samburu region of northern Kenya, the problem of culling elephants in Kruger National Park, the overexploitation of fisheries, circumcision as an intervention for managing HIV, and the impact of HIV on the reemergence of TB.
The Hodgkin-Huxley model of the action potential is a landmark of twentieth century biology. Mathematical analysis of even simplified versions of this model encounters surprisingly subtle phenomena involving the bifurcations of dynamical systems with multiple time scales. This lecture will survey recent mathematical research in this area and speculate on its biological implications.
Vascular endothelial growth factor (VEGF) is one of the most potent, specific and intensively studied tumor angiogenic factors. Recent experiments show that VEGF is the crucial mediator of downstream events that ultimately lead to enhanced endothelial cell survival and increased vascular density within many tumors. The newly discovered pathway involves up-regulation of the anti-apoptotic protein Bcl-2, which in turn leads to increased production of interleukin-8 (CXCL8). The VEGF-BCL2-CXCL8 pathway suggests new targets for the development of anti-angiogenic strategies including short interfering RNA (siRNA) that silence the CXCL8 gene and small molecule inhibitors of Bcl-2. In this talk I will discuss our efforts to develop and validate mathematical models of sustained angiogenesis and vascular tumor growth that are able to predict the effect of the therapeutic blockage of VEGF, CXCL8, and Bcl-2 at early middle and late stages of tumor progression.
Transient or unstable behavior is often ignored in considering long time dynamics in the deterministic world. However, stochastic effects can change the picture dramatically, so that the transients can dominate the long range behavior. Coherence resonance is one relatively simple example of this transformation, and we consider others such as noise-driven synchronization in networks, disease dynamics in vaccinated populations, and amplitude-driven phase dynamics. The challenge is to identify common features in these phenomena, leading to new approaches for systems of this type. Some recurring themes include the influence of multiple time scales, cooperation of both discrete and continuous aspects in the dynamics, and the remnants of underlying bifurcation structure visible through the noise.
The coalescent is a mathematical object that describes the genealogy of a random sample of genes from a very large population. Kingman defined this process in 1982 and it has since become a standard tool in the analysis of population data. Kingman formulated the process under the assumption of neutrality. This process was later extended to selection in Neuhauser and Krone (1997). A critical assumption in all these models is that populations evolve in the absence of ecological forces. We will provide an overview of some of the established mathematical theory and then address how to incorporate ecological forces into the genealogy.
We analyze a model of gene transcription and protein synthesis which has been previously presented in the biological literature. The biology of the problem may be described as follows: A gene, i.e. a section of a DNA molecule, is copied (transcribed) into messenger RNA (mRNA), which is transported out of the nucleus of the cell into the cytoplasm, where it enters a subcellular structure called a ribosome. In the ribosome the genetic information encoded in the mRNA produces a protein (a process called translation). The protein then enters the nucleus where it represses the transcription of its own gene.
The model takes the form of an ODE (ordinary differential equation) coupled to a DDE (delay differential equation), the state variables being concentrations of messenger RNA and protein. Sources of the delay include the time required for transcription and translation to occur. The delay is assumed to depend on the concentration of mRNA and is therefore state dependent. Linear analysis gives a critical time delay beyond which a periodic motion is born in a Hopf bifurcation. Lindstedt's method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation. Results of the perturbation method are shown to be in good agreement with those obtained by numerical integration.
This work is joint with Anael Verdugo, a graduate student in the Center for Applied Math at Cornell University.
One-carbon metabolism, consisting of the folate cycle, the methionine cycle, and glutathione synthesis is a small part of cell metabolism, but it is crucial for cell division, DNA methylation, and the manufacture of glutathionine, the body's defense against oxidative stress. Deficiencies in one-carbon metabolism have been associated with important human health concerns including heart disease, some cancers, depression, and birth defects. We will describe a number of biochemical control mechanisms that insure that important reactions in one-carbon metabolism are protected against large variations in dietary input. These mechanisms are analyzed by studying how stochastic fluctuations propagate through biochemical networks.
The dynamics of a disease transmitted by a vector from one individual host to the other is studied. The impact of eliminating or limiting the total number of disease-transmitting agents, treating the infected hosts and implementing prevention mechanisms on the overall effort of controlling the disease is considered. The study also looks into the effects of some additional factors such as, the transmission of the disease from vector-to-vector, then to a host via the surrounding media. Analytical approach is used to get local and global stability of equilibrium points.
We introduce a recursive algorithm which enables the computation of the distribution of epidemic size in a stochastic SIR model for very large population sizes. In the important parameter region where the model is just slightly supercritical the distribution of epidemic size is decidedly bimodal. We find close agreement between the distribution for large populations and the limiting case where the distribution is that of the time a Brownian motion hits a quadratic curve. The model includes the possibility of vaccination at a constant rate during the epidemic. The effects of the parameters, including vaccination level, on the form of the epidemic size distribution are explored.
Background: The latest avian influenza virus classified as H5N1 has raised significant global concern about its potential to cause a pandemic of catastrophic proportions. Since vaccine is likely to be unavailable in the early phases of a pandemic, and limited stockpiles of antiviral medications may be ineffective against the new strain, non-pharmaceutical interventions will play a key role in controlling the spread of influenza.
Methods and Findings: We use an agent-based simulation model to assess the impact of behavioral changes during a pandemic. In particular, we analyze the impact that school closures, fear-based home isolation, and social distancing can have on the spread of influenza. We demonstrate that both temporary and permanent behavioral modifications can reduce the transmission of the disease. However, temporary behavioral changes have the potential to generate waves, if they are relaxed before the pandemic dies out.
Conclusions: We show that individual and community-based behavioral modifications can have a significant effect on slowing influenza spread and reducing morbidity and mortality. However, temporary behavioral changes can create susceptible populations, resulting in waves. Thus, planning should be done in advance, so that policies regarding recommendations on behavioral changes would be achievable and maintainable by the parties involved.
Influenza A virus (IAV) infection is an important cause of morbidity and mortality, especially among the very young, the elderly, and the immuno-compromised. Presently, there is a need for quantitative models that would, for example, shed light on the in vivo dynamics of the IAV, enable systematic assessment of the efficacies of current anti-IAV therapies, and, possibly, inform the development of improved strategies for managing IAV infection. A simple mathematical model of the in vivo dynamics of the IAV was developed. The model accounts for the heterogeneity in intracellular IAV dynamics mediated by (1) interferon priming of naive host cells and (2) the (functional) quasispecies nature of the virus. The model was fitted to data on primary IAV infection of human subjects, and parameters relevant to the viral dynamics were estimated. These parameters include the half-life of productively infected cells, the mean number of secondary infections produced by an infected cell, the rate constants for viral infection of interferon-primed and unprimed cells, and the rate of clearance of cell-free virions. The model was also used to estimate the efficacies of the commonly used anti-IAV drugs, oseltamivir and zanimivir, using clinical trial data.
Recurrent avian flu cases in humans, arising primarily 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 basic public health control measures for minimizing transmission in hospitals and communities, the use of antiviral drugs, and vaccination. This paper presents a mathematical model for the evaluation of the pandemic flu preparedness plans of the United States (US), the United Kingdom (UK) and the Netherlands. The model is used to assess single and combined interventions. Using data from the US, we show 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 lead to very significant reductions in the burden of a pandemic, the combination of transmission control measures, antivirals and vaccine gives the most ``optimal'' result. However, implementing such an optimal strategy at the onset of a pandemic may not be realistic. Thus, it is important to consider other plausible alternatives. An optimal preparedness plan is largely dependent on the availability of resources; and, hence, it is country--specific. We show that for antiviral interventions, countries with limited supplies should emphasize their use therapeutically (rather than prophylactically). However, countries with large antiviral supplies can achieve greater reductions 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 the Netherlands. It emphasizes the importance of hospital and community transmission control measures in addition to the timely use of antiviral treatment in reducing the burden of a potential flu pandemic. The latter is consistent with the preparedness plans of the UK and the Netherlands. Our results indicate that a single-inte rvention program based on the use of vaccination seems to have limited impact in comparison to that based on the use of antivirals.
In this paper we study the existence of traveling wave solutions for an integro-differential system of equations. The system was proposed by Lin et. al as a model for the spread for influenza A drift. The model uses diffusion to simulate the mutation of the virus along a one dimensional phenotype space. By considering the system under the traveling wave variable z=x-ct the PDE system is transformed to a higher dimensional ODE system. Applying the theory of geometric singular perturbation we constructed a traveling wave solution for the system.
Mixing patterns drive the transmission of infectious diseases. Different mixing assumptions have different impacts on the spread of pandemic influenza and propose interventions strategies that could affect the overall attack rate at different social contexts. We use the agent-based stochastic simulation model, EpiSimS and modify the hourly interactions of the population at different locations. Our results show that the disease is most sensitive to changes in the hourly interactions at work locations. Approximately 60% of the total infected population are between the ages 19 and 64, which is the working population; therefore, social distancing at work maybe useful to halt the spread of pandemic influenza in communities in which the working population is the largest.