Susceptibles-infectives-removals (SIR) and its derivatives are the classic mathematical models for the study of infectious diseases in epidemiology. In order to model and simulate epidemics of an infectious disease, a global stochastic field simulation paradigm (GSFS) is proposed, which incorporates geographic and demographic based interactions. The interaction measure between regions is a function of population density and geographical distance, and has been extended to include demographic and migratory constraints. The progression of diseases using GSFS is analyzed, and similar behavior to the SIR model is exhibited by GSFS, using the geographic information systems (GIS) gravity model for interactions. The limitations of the SIR and similar models of homogeneous population with uniform mixing are addressed by the GSFS model. The GSFS model is oriented to heterogeneous population, and can incorporate interactions based on geography, demography, environment and migration patterns. The progression of diseases can be modeled at higher levels of fidelity using the GSFS model, and facilitates optimal deployment of public health resources for prevention, control and surveillance of infectious diseases.

Computational modeling is of fundamental significance in mapping possible disease spread, and designing strategies for its mitigation. Conventional contact networks implement the simulation of interactions as random occurrences, presenting public health bodies with a difficult trade off between a realistic model granularity and robust design of intervention strategies. Recently, researchers have been investigating the use of agent-based models (ABMs) to embrace the complexity of real world interactions. At the same time, theoretical approaches provide epidemiologists with general optimization models in which demographics are intrinsically simplified. The emerging study of affiliation networks and co-affiliation networks provide an alternative to such trade off. Co-affiliation networks maintain the realism innate to ABMs while reducing the complexity of contact networks into distinctively smaller k-partite graphs, were each partition represent a dimension of the social model. This dissertation studies the optimization of intervention strategies for infectious diseases, mainly distributed in school systems. First, concepts of synthetic populations and affiliation networks are extended to propose a modified algorithm for the synthetic reconstruction of populations. Second, the definition of multi-coaffiliation networks is presented as the main social model in which risk is quantified and evaluated, thereby obtaining vulnerability indications for each school in the system. Finally, maximization …

The history of mitigation programs to contain vector-borne diseases is a story of successes and failures. Due to the complex interplay among multiple factors that determine disease dynamics, the general principles for timely and specific intervention for incidence reduction or eradication of life-threatening diseases has yet to be determined. This research discusses computational methods developed to assist in the understanding of complex relationships affecting vector-borne disease dynamics. A computational framework to assist public health practitioners with exploring the dynamics of vector-borne diseases, such as malaria and dengue in homogenous and heterogeneous populations, has been conceived, designed, and implemented. The framework integrates a stochastic computational model of interactions to simulate horizontal disease transmission. The intent of the computational modeling has been the integration of stochasticity during simulation of the disease progression while reducing the number of necessary interactions to simulate a disease outbreak. While there are improvements in the computational time reducing the number of interactions needed for simulating disease dynamics, the realization of interactions can remain computationally expensive. Using multi-threading technology to improve performance upon the original computational model, multi-threading experimental results have been tested and reported. In addition, to the contact model, the modeling of biological processes specific to …