Reaction-diffusion process and the modeling of the spatial spread of infectious diseases

The reaction-diffusion (R-D) process is a fundamental modeling approach over a wide range of physical systems. It is applicable to a variety of dynamical process which local quantities diffuse and react according to physical laws, such as particle systems, infectious diseases, and computer malwares. The dissertation mainly focuses on modeling infectious disease spreading using such process on realistic heterogeneous networks and study their spatial-temporal diffusive behaviors.;To give an example of how R-D process can be applied to the domain of epidemic modeling, it is first applied to a tightly interconnected proximity WiFi router network in urban areas. Given the reverent security flaws on these WiFi routers, they can be exploited as a substrate for the spreading of malwares. Several scenarios are considered for the deployment of malware that spreads over the wireless channel of major urban areas in the US. The spread of such a contagion is simulated on real-world data for georeferenced wireless routers. We uncover a major weakness of WiFi networks in that most of the simulated scenarios show the majority of the infections occurring in the first 24-48 hours. We indicate possible containment and prevention measures and provide computational estimates for the rate of encrypted routers that would stop the spreading of the epidemics by placing the system below the percolation threshold.;Next, the construction details of Global Epidemic and Mobility (GLEaM) model is demonstrated, which integrates socio-demographic and population mobility data in a spatially structured stochastic reaction-diffusion disease modeling approach to simulate the spread of epidemics at the worldwide scale. It is aimed at understanding historical epidemics, identifying key mechanisms and spreading patterns, predicting future scenarios and assessing the efficacy of interventions. Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. We also report the interplay between short-scale commuting flows and long-range airline traffic in shaping the spatiotemporal pattern of a global epidemic, defining layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multiscale framework.;Finally, GLEaM is used to predict the seasonal transmission potential and the activity peaks of the 2009 Influenza A(H1N1) during Summer, 2009. In order to estimate the transmission potential and the relevant model parameters we used the data on the chronology of the 2009 novel influenza A(H1N1). The method is based on the maximum likelihood analysis of the arrival time distribution generated by the model in 12 countries seeded by Mexico by using 1 million computationally simulated epidemics. An extended chronology including 93 countries worldwide seeded before 18 June was used to ascertain the seasonality effects. The Monte-Carlo likelihood analysis showed ahead of time the potential for an early epidemic peak occurring in October/November 2009 in the Northern hemisphere, before large-scale vaccination campaigns carried out. The simulated results are in good agreement with the later empirical observations throughout influenza season. We also provide estimates of the size of the epidemic in Mexico as well as of imported cases at the end of April and beginning of May. We find that the reference range for the number of cases in Mexico on April 30th is in good agreement with the recent estimates, and the number of imported cases from Mexico in several countries is found to be in good agreement with the surveillance data.