Mathematical Models for Understanding the Effect of Long-Range Interactions and Intervention Measures on the Spread of Epidemics

Cuny City College, New York NY

Investigators

Abstract

Developing efficient and cost-effective intervention and monitoring strategies for preventing the spread of infection in the plant and human world requires an understanding of the underlying mechanisms by which infection spreads spatially and temporally, and of the quantitative effect of different intervention strategies. In the case of plant pathogens, long-distance dispersal phenomena and spatial heterogeneity of infection spreading can lead to failure of disease-control strategies that are based on naive models. Furthermore, such weak control strategies are often uneconomical and use copious amounts of pesticides on crops. In the case of human-contagious diseases, better intervention strategies can be developed if quantitative effects of quarantine are known. By analyzing spatial epidemic models with long-distance dispersal and certain intervention strategies, this research project aims to provide new insights into the mechanistic underpinning of dispersal on features of plant epidemics, and into the effects of quarantine strategies on restraining the spread of contagious infection among humans. To guarantee that the results are relevant to epidemiology, a part of the project will be carried out in collaboration with ecologists and epidemiologists. The involvement of undergraduate and graduate students in this research will enhance their ability to work at the interface between mathematics and biology. This project addresses challenges in developing more effective and economical intervention strategies for preventing the spread of infection in the plant and human world. Most of the epidemic models that have been analyzed rigorously to investigate the role of space in infection spreading are nearest-neighbor in nature. However, there are many plant diseases where the infection spreads via long-distance dispersals. To understand the effect of long-distance dispersal on infection spreading, several complex agent-based models have been analyzed using simulation and some heuristic methods in the theoretical biology literature. These non-rigorous treatments of the epidemic models sometimes lead to erroneous conclusions. One of the primary goals of this project is to understand rigorously the effect of long-range interactions on the spread of infections and associated features. In this project, the investigator plans to study several aspects of long-range first-passage percolation models by adding "long-range interaction" features to the standard (nearest-neighbor) first-passage percolation models. The investigator also plans to study intervention strategies for SIS models, which are frequently used for modeling spread of recurring disease among humans, in one dimension and on complex heterogeneous graphs. The rigorous analyses of these models will require the development of novel mathematical techniques. These techniques are expected to lead to a deeper understanding of a broad class of spatial stochastic epidemic models. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.