The relatively benign human influenza virus strain that infects many of us year-round, albeit with seasonal pulses in frequency, can sometimes evolve into a potentially deadly strain that is capable of triggering a pandemic. The three recent human flu pandemics of 1918, 1957 and 1968--respectively known as the "Spanish flu", "Asian flu", and "Hong Kong flu"--caused huge devastation both in terms of the loss of human lives and consequent economic impacts. For each of these, genetic evidence suggests that a novel influenza strain evolved from the genetic recombination ("shift") of an animal flu strain and a human flu strain within a common host species that was co-infected by these two strains. This newly evolved strain had catastrophic effects on humans because of the absence of natural immunity by the host to this strain. The recent cases of human infection and death from avian influenza virus in several parts of the world, and the fact that humans and other animal species (such as swine) can act as a shared host to both avian flu and human flu strains, has raised concern that we may face a near-term emergence of another novel and highly virulent strain, thus another potential pandemic. Mathematical models provide crucial tools for understanding and possibly predicting and controlling the emergence and subsequent spread of novel pathogen strains. In this project we develop and analyze mathematical and simulation models to study real-world biological scenarios, in which there is co-infection of human host by avian flu and human flu strains. We will focus in particular on characterizing conditions for invasion and persistence of emergent virulent strains within human populations. This project will significantly advance our knowledge of the transmission dynamics and evolution of avian influenza from bird to human populations in particular, and of multi-species epidemic systems in general. It will provide a series of usable, realistic models that are grounded on available data. These models can serve as a solid background for future extensions incorporating and testing the efficacy of various control measures (such as vaccination, chemotherapy, and social distancing) for pandemic influenza, and suggest avenues of empirical study that are particularly important to pursue for disease prediction.
In terms of technical approaches, this project unites the efforts of mathematicians and biologists in developing models based on integrated partial differential equations (PDE), ordinary differential equations (ODE), and stochastic individual-based simulations (IBS), to study the evolutionary epidemiology and population biology of avian influenza (AI). The research goal will be pursued along two main directions. 1) The "drift" and "shift" mechanisms of genomic evolution of an influenza virus will be simultaneously incorporated within a multi-strain PDE model that then will be used to predict the epidemiological consequences in a human population of an evolved influenza variant -- a novel avian influenza strain with both high pathogenicity and high human-to-human transmission efficiency. ODE versions of this model will be fitted to available World Health Organization (WHO) data of the cumulative number of human cases of avian influenza infection. Mathematical analysis of the best fitting ODE and PDE models will then be carried out, to rigorously characterize conditions for spread and persistence. 2) Complementary individual-based simulation (IBS) models of a human population will be developed on a small-world type network that incorporate explicit social interaction (contact) neighborhoods of each individual, and stochastic processes of birth, death and infection events. The pattern of flu outbreaks in these IBS models will be studied with respect to the underlying network structure, and related to the predictions of the corresponding ODE models. This will help elucidate the role of stochastic factors likely to be important in the early stages of strain emergence.
Avian influenza (bird flu) primarily infects wild and domestic birds. Since 1997, it has also started to infect humans through bird-to-human transmission (especially to people working with poultry). Thus far there have been more than 600 humans infected, 60% of whom have died. The most serious public health threat that avian influenza poses to humans is the potential appearance of a human-to-human transmittable strain that could cause a deadly pandemic. The chance of appearance of such a strain increases as more people and poultry become infected. Mathematical modeling provides an understanding of the complex epidemiology of avian influenza and a tool for evaluating the effect of multiple control measures. As a result of this award a number of mathematical models of avian influenza were developed. The predictions of these models were compared with data that the World Health Organization collects on human cases. It was found that these models not only agree well with past data, but are capable of forecasting future data, giving us the ability to estimate the number of future human cases of avian influenza, including under various control measure scenarios. Furthermore, the mathematical models created as part of this award can help evaluate the pre-pandemic control measures currently used to reduce the prevalence of the disease. In particular, they showed that control measures applied to poultry, such as culling and vaccination, are much more efficient in reducing the number of human cases than control measures applied to humans, such as wearing protective gear. In fact, these models suggested that culling (without replacement of the killed birds) and vaccination of poultry are the two most efficient control measures applied today. Prior research reports on avian influenza have suggested that culling in case of a pandemic may facilitate the invasion of the pandemic strain. We quantified this effect and it to be very weak. In particular, decreasing the prevalence (the number of individuals infected) of avian influenza in poultry by 1% increases the invasion capabilities of the pandemic strain by 0.06%. We also find that human influenza prevalence has a more significant impact on the invasion capabilities of the pandemic strain. Mathematical techniques that evaluate how the solutions of our avian influenza models behave have been developed. This has led to the derivation of biologically meaningful general conditions for various outcomes. The PI and her team have written a number of computer programs, some that perform the fitting of our models to data, and some that simulate avian influenza models that include age structure. This award has assisted in the training of five US graduate students, one of whom is a minority. Two of those graduate students have obtained their PhD by the end of this award. As part of the activities, two US students visited China to work on research with Chinese students and faculty and two Chinese students/faculty visited the US and worked with the US students and faculty. The award has further trained two post-doctoral associates, one in mathematics and one in biology. Twenty research articles have been published or are in the process of being published. Twenty-four talks and posters have been given at national and international meetings in the US and abroad. The PI has taught a Mathematical Epidemiology class to graduate students, and has covered techniques developed as part of this award for fitting models to data, as well as mathematical tools for the investigation of avian influenza models, and the co-PI has likewise given graduate courses including aspects of this material. The PI has also taught a graduate/undergraduate class in Modeling in Mathematical Biology that incorporated avian influenza models. The PI has written several chapters of a graduate level textbook in Mathematical Epidemiology that will incorporate models and techniques developed as part of this award. An avian influenza web-site has been created and maintained throughout the award. The web-site contains links to avian influenza data and data on poultry. It also features a figure that shows the best avian influenza model fit to the cumulative number of human cases and a comparison of the projections with incoming data. An avian influenza blog has also been started and maintained throughout part of the award. The blog featured results from the avian influenza research performed under this award.
