We present an analysis of two features that generalize the original
model for the spread of the Hantavirus introduced by Abramson and Kenkre [Phys. Rev. E Vol. <b>66</b>, 011912 (2002)]. One, the effect of seasonal alternations, may cause the virus to spread under conditions that do not lead to an epidemic under the action of either season alone. The other, the effect of internal fluctuations, modifies
the distribution of infected mice and may lead to extinction of the infected population even when the mean population is above epidemic conditions.
We present a comprehensive study of phase transitions in single-field extended systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift but is instead similar to the one associated with noise-induced transitions <i>a la</i> Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Ito vs Stratonovich) merely shifts the phase boundaries. With the help of a mean-field approximation, we present a broad qualitative picture of the various phase diagrams that can be found in these systems.
We review the critical patch size problem, already classic in the mathematical biology literature. We consider a logistic population
living in a finite patch of length L and undergoing random dispersal. The patch presents good conditions for life, while the conditions are so harsh outside that they lead to certain extinction. The usual mean field approach leads to a critical patch size <i>L<sub>c</sub></i>, such that if the actual length of the patch is smaller than <i>L<sub>c</sub></i> the population becomes extinct with certainty, whereas a longer patch leads to certain survival. We study the fluctuations in the population due to its low density near extinction and analyze their effects on the probability of extinction. We find that there is no patch size that can be considered absolutely safe for the population and that, under certain circumstances, the population is under risk of extinction for any patch size.
We revisit the issue of directed motion induced by zero average forces in extended systems driven by ac forces. It has been shown recently that a directed energy current appears if the ac external force, <i>f</i>(<i>t</i>), breaks the symmetry <i>f</i>(<i>t</i>) = -<i>f</i>(<i>t</i>+<i>T</i>/2), <i>T</i> being the period, if topological solitons (kinks) existed in the system. In this work, a collective coordinate approach allows us to identify the mechanism through which the width oscillation drives the kink and its relation
with the mathematical symmetry conditions. Furthermore, our theory predicts, and numerical simulations confirm, that the direction of motion depends on the initial phase of the driving, while the system behaves in a ratchet-like fashion if averaging over initial conditions. Finally, the presence of noise overimposed to the ac driving does not destroy the directed motion; on the contrary, it gives rise to an activation process that increases the velocity of the motion. We conjecture that this could be a signature of resonant phenomena at larger noises.