A generalized model of the spread of the Hantavirus in mice populations is presented on the basis of recent observational findings concerning the movement characteristics of the mice that carry the infection. The factual information behind the generalization is based on mark-recapture observations reported in Giuggioli et al. [Bull. Math. Biol. 67 1135(2005] that have necessitated the introduction of home ranges in the simple model of Hantavirus spread presented by Abramson and Kenkre [Phys. Rev. E 66 11912 (2002)]. The essential feature of the model presented here is the existence of adult mice that remain largely confined to locations near their home ranges, and itinerant juvenile mice that are not so confined, and, during their search for their own homes, move and infect both other juveniles and adults that they meet during their movement. The model is presented at three levels of description: mean field, kinetic and configuration. Results of calculations are shown explicitly from the mean field equations and the simulation rules, and are found to agree in some respects and to differ in others. The origin of the differences is shown to lie in spatial correlations. It is indicated how mark-recapture observations in the field may be employed to verify the applicability of the theory.
Abstract. The role of forest heterogeneity in the long-term, large-scale dynamics of forest fires is investigated by means of a cellular automata model and mean field approximation. Heterogeneity was conceived as trees (or acres of forest) with distinct strengths of resistance to burn. The scaling analysis of fire-size and fire-lifetime frequency distributions in the non-interacting fire steady-state limit indicates the breakdown of the power-law behavior whenever the resistance strength parameter R exceeds a certain value. For higher resistant strength, exponential behavior characterizes the frequency distributions, while power-law like behavior was observed for the lower resistant case in the same manner as reported in the literature for a homogeneous counterpart model. For the intermediate resistance strength, however, it may be described either by a stretched exponential or by a power-law plot whenever the fraction of recovering empty cells by susceptible trees not-exceeds or exceeds a certain threshold respectively, also suggesting a dynamical percolation transition with respect to the stationary forest density.
The local properties of the spin one ferromagnetic Blume-Capel model defined on hierarchical lattices with dimension two and three are obtained by a numerical recursion procedure and studied as functions of the temperature and the reduced crystal-field parameter. The magnetization and the density of sites in the configuration S = 0 state are carefully investigated at low temperature in the region of the phase diagram that presents the phenomenon of phase reentrance. Both order parameters undergo transitions from the ferromagnetic to the ordered paramagnetic phase with abrupt discontinuities that decrease along the phase boundary at low temperatures. The distribution of magnetization in a typical profile was determined on the transition line presenting a broad multifractal spectrum that narrows towards the fractal limit (single point) as the discontinuities of the order parameters grow towards a maximum. The amplitude of the order-parameter discontinuities and the narrowing of the multifractal spectra were used to delimit the low temperature interval for the possible locus of the tricritical point.
The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest like cellular automaton model with two distinct populations of cells (permissive and resistant ones) and studied in the framework of the mean field approximation. Stochastic dynamical ingredients are introduced into this model to mimic cells regeneration (with probability p) and to consider infection processes by other means than contiguity (with probability f). Simulations are carried out on a L×L square lattice taking into consideration the eighth first neighbors. The mean density population of infected cells (Di) is measured as a function of the regeneration probability p, and analyzed for small values of the ratio f/p and for distinct degrees of cell resistance. The results obtained by a mean field like approach recovers the simulations results. The role of the resistant parameter R (R≥2) on the steady state properties, is investigated and discussed in comparison with the R=1 monocell case which corresponds to the self organized critical forest model. The fractal dimension of the dead cells ulcers contours was also estimated and analyzed as a function of the model parameters.
Effects of predators of juvenile mice on the spread of the Hantavirus are analyzed in the context of a recently proposed model. Two critical values of the predation probability are identified. When the smaller of them is exceeded, the hantavirus infection vanishes without extinguishing the mice population. When the larger is exceeded, the entire mice population vanishes. These results suggest the possibility of control of the spread of the epidemic by introducing predators in areas of mice colonies in a suitable way so that such control does not kill all the mice but lowers the epidemic spread.
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