Naser Alqutaifi | Applied Math, University of Waterloo
Networks and the Epidemiology of Infectious Disease
Infectious diseases remain a major cause of illness and death in the world today. One of the major reasons for studying infectious diseases is to improve control and ultimately to eradicate the infection from the population. The earliest account of Mathematical modelling in epidemiology (the study of health and disease in human population), going back to the eighteenth century (Bernoulli 1760). Special models have been created for diseases like smallpox, malaria, AIDS, SARS, cholera, etc.
Networks tend to be very powerful tools for understanding the transmission of infection in human populations due to either social contacts (for airborne infections) or sexual contacts (for sexually transmitted diseases). When looking into real-world complex networks, however, one can find many instances of networks whose states and topologies “coevolve”, i.e., they interact with each other and keep changing, often over the same time scales, due to the system’s own dynamics. Modeling and predicting state-topology coevolution is now becoming well recognized as one of the most significant challenges in complex network research.
Most studies have not considered the effects of interactions between network structure and individual learning behavior, and assume that the population is homogeneously mixed and that individuals are fully rational such that they make decisions to pursue maximum personal utility based on their perceived risks. In reality, there is always a spatial structure on which both the disease transmission and individual contacts take place. Individuals may be limited rational. Under heterogeneous network, the influence of everybody is different.
All processes take time to complete. In realistic systems, we cannot neglect the time delay, such as period during which the epidemic recovers and information transmitting interval, etc.. The models that incorporate such delay times are referred as delay differential equation (DDE) models. Time-delay systems widely exist in engineering and science, where the rate of change of state is determined by both present and past state variables. Recently, multiple time delays are introduced to complex dynamical networks. So, our aim is to study different epidemic models with multiple-time delays on complex networks.
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