Individual-based lattice model for spatial spread of epidemics

We present a lattice gas cellular automaton (LGCA) to study spatial and temporal dynamics of an epidemic of SIR (susceptible-infected-removed) type. The automaton is fully discrete, i.e. space, time and number of individuals are discrete variables. The automaton can be applied to study spread of epidemics in both human and animal populations. We investigate effects of spatial inhomogeneities in initial distribution of infected and vaccinated populations on the dynamics of epidemic of SIR type. We discuss vaccination strategies which differ only in spatial distribution of vaccinated individuals. Also, we derive an approximate, mean-field type description of the automaton, and discuss differences between the mean-field dynamics and the results of LGCA simulation.Comment: 13 pages, 5 figure

Effects of population mixing on the spread of SIR epidemics

We study dynamics of spread of epidemics of SIR type in a realistic spatially-explicit geographical region, Southern and Central Ontario, using census data obtained from Statistics Canada, and examine the role of population mixing in epidemic processes. Our model incorporates the random nature of disease transmission, the discreteness and heterogeneity of distribution of host population. We find that introduction of a long-range interaction destroys spatial correlations very easily if neighbourhood sizes are homogeneous. For inhomogeneous neighbourhoods, very strong long-range coupling is required to achieve a similar effect. Our work applies to the spread of in influenza during a single season and our model is applicable to other geographic regions, if suitable data is available

Charge-transfer in time-dependent density-functional theory via spin-symmetry-breaking

Long-range charge-transfer excitations pose a major challenge for time-dependent density functional approximations. We show that spin-symmetry-breaking offers a simple solution for molecules composed of open-shell fragments, yielding accurate excitations at large separations when the acceptor effectively contains one active electron. Unrestricted exact-exchange and self-interaction-corrected functionals are performed on one-dimensional models and the real LiH molecule within the pseudopotential approximation to demonstrate our results.Comment: 5 pages, 4 figure

Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of non-equilibrium dynamical situations relevant for modeling of photo-chemical/physical processes: field-free evolution of a non-stationary state, resonant local excitation, resonant complete charge-transfer, and evolution under an arbitrary field. Lack of these steps in usual approximations yield inaccurate dynamics, for example predicting faster dynamics and incomplete charge transfer