# A PhD in the DAAD Program “Mathematics in Industry and Commerce”

## Agent Based Modeling of Spatially Inhomogeneous Host-Vector Disease Transmission

In recent years disease transmission has been studied intensively. In these models, disease transmission represents the contact between host individuals in directly transmitted diseases, or between host and vector individuals in host-vector diseases. A series of diﬀerent models for vector-bourne diseases such as Dengue fever including stochastic and deterministic models, fractional diﬀerential equation or the eﬀect of climate to the mosquito have been proposed. The models described do not provide any information about the spatial spread of a disease. Nevertheless, there have been various approaches to link many diﬀerent SIR-areas to obtain spatial behavior. In the SIR-model case, an advection-diﬀusion equation has been identiﬁed as the limiting equation. On the macroscopic level, the models are very ﬂexible for describing the diﬀerent aspects of disease dynamics. However, for many diﬀerent diseases the infection mechanism is only known on the microscopic, i.e., agent-to-agent level. To consider both microscopical modeling and spatial resolution, we describe the disease dynamics by means of an interacting particle system with suitable interaction potentials. Fundamental in this area are dynamics in so-called marked conﬁguration spaces. These techniques together with a proper scaling of the microscopic system, the so-called Vlasov scaling, have been recently used to model the dynamics of cancer cells.

We set up a microscopic model for the host- vector disease transmission based on conﬁguration space analysis and wee model transmission with birth-death in vector and mobility in host. In our model the prescribed ﬂip from a healthy host (vector) getting infected by the surrounding infected vectors (hosts), with R ∈ (0, ∞) denotes the maximal distance of possible infection for a single healthy indi- vidual at direct contact with an infected one. Numerically, the spread of the disease is shown in the following Susceptible hosts are depicted as green spots, infected hosts as red spots, susceptible vectors as blue spots, and infected vectors as orange spots.

This PhD is done in the framework of the DAAD Program “Mathematics in Industry and Commerce” in the Department of Mathematics at the TU Kaiserslautern. For more information contact Isti Rodiah (rodiah@mathematik.uni-kl.de).