Biological populations and epidemic spreading: stochastic and spatially structured modeling

We will address topics covered by the stochastic dynamics, which are inserted in the field of statistical physics of non-equilibrium. The issues we will fix concern the modeling of biologically motivated systems. Topics to be visited consist primarily those related to the dynamics of biological populations as well as those related to spread of epidemics. To this end, we will consider irreversible models described by a Master equation and probabilistic cellular automata. Among the epidemic models to be discussed are: the Susceptible-Infected-Recovered system (SIR) described by a master equation; and a model to describe the stochastic dynamics for dengue epidemic. Among the models for biological populations is a stochastic lattice model to describe the coexistence of predators and prey in a habitat. This coexistence may be accompanied by fluctuations in the populations of each species. We will talk over the nature and characterization of these oscillations. We intend to explore the spatiotemporal patterns related to population dynamics. In addition, we analyze the dynamical and static critical behavior and universality classes associated to non-equilibrium phase transitions, which may occur in these systems.
References
(1)T?nia Tom? and M. J. de Oliveira, Stochastic Dynamics and Irreversibility, Springer, 2015.
(2)D. R. de Souza, T?nia Tom?, S. Pinho and F. Barreto, Phys. Rev. E 87, 012709 (2013).
(3)T?nia Tom? and R. M. Ziff, Phys. Rev. E 82 051921 (2010).
(4)T. Tom?, A. L. Rodrigues, E. Arashiro and M. J. de Oliveira, Comput. Phys. Comm 180, 536 (2009).