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Register a new userCritical behavior of an epidemic model of drug resistant diseases
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In this work, we study the critical behavior of an epidemic propagation model that considers individuals that can develop drug resistance. In our lattice model, each site can be found in one of four states: empty, healthy, normally infected (not drug resistant) and strain infected (drug resistant) states. The most relevant parameters in our model are related to the mortality, cure and mutation rates. This model presents two distinct stationary active phases: a phase with co-existing normal and drug resistant infected individuals and an intermediate active phase with only drug resistant individuals. We employ a finite-size scaling analysis to compute the critical points the critical exponents ratio $beta/ u$ governing the phase-transitions between these active states and the absorbing inactive state. Our results are consistent with the hypothesis that these transitions belong to the directed percolation universality class.
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We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.
Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually rely on mental maps to explore strongly heterogeneous environments. In this work we study a model of a deterministic walker, visiting sites randomly distributed on the plane and with varying weight or attractiveness. At each step, the walker minimizes a function that depends on the distance to the next unvisited target (cost) and on the weight of that target (gain). If the target weight distribution is a power-law, $p(k)sim k^{-beta}$, in some range of the exponent $beta$, the foraging medium induces movements that are similar to Levy flights and are characterized by non-trivial exponents. We explore variations of the choice rule in order to test the robustness of the model and argue that the addition of noise has a limited impact on the dynamics in strongly disordered media.
We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a non trivial fixed point which is stable for $0.995<a<2$ and is characterized by the correlation length exponent $ u= 2/a + O((2-a)^3)$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent $eta_2=1/2-(2-a)/4+O((2-a)^2)$.
We introduce a 2-layer network model for the study of the immunization dynamics in epidemics. Spreading of an epidemic is modeled as an excitatory process in a small-world network (body layer) while immunization by prevention for the disease as a dynamic process in a scale-free network (head layer). It is shown that prevention indeed turns periodic rages of an epidemic into small fluctuation. The study also reveals that, in a certain situation, prevention actually plays an adverse role and helps the disease survive. We argue that the presence of two different characteristic time scales contributes to the immunization dynamics observed.
We study an S--I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic equilibrium. We obtain conditions on the age-dependence of the susceptibility to infection that imply the uniqueness of the endemic equilibrium. An example with two endemic equilibria is shown. Finally, we analyse numerically how the stability of the endemic equilibrium is affected by extra-mortality and by the possible periodicities induced by the demographic age-structure.
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