An Agent Based Modeling of Disease Transmission in the Framework of Configuration Spaces

This thesis considers a microscopic model for disease transmission based on configuration space analysis. Two types of disease spreading are considered in this research, i. e., the direct contact transmission and the host-vector transmission. We also model transmission with birth, death, and mobility of particles. Using Vlasov scaling, we obtain the corresponding mesoscopic (kinetic) equations, describing the density of susceptible and infected compartment in space. The resulting system of equations can be seen as a generalization to a spatial disease model. The particle and kinetic models are investigated numerically. The time fractional derivative is applied to the kinetic description and describes the sub-diffusion process in disease dynamics. Furthermore, the estimation of the basic reproduction ratio is developed from the kinetic equations. In this approach, we may obtain the local and global threshold of infectious disease.