Abstract
The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.
Highlights
The study of epidemic outbreaks is a largely interdisciplinary topic
The analysis of[10] is based on the Master Equation formulation of the stochastic dynamics: d P (Λ; t) = ∑w (Λ′ → Λ) P (Λ′; t) − ∑w (Λ → Λ′) P (Λ; t), dt where P(Λ; t) is the probability that the full-lattice vector-mediated epidemics (VME) model is in the state Λat time t, and w(Λ→Λ′) are the rates of the configuration change Λ→Λ′
We have improved the determination of the critical line exhibited by the VME model proposed in[10] and identified the character of the transition along the whole line, showing that the model has the critical exponents as standard dynamical percolation
Summary
The study of epidemic outbreaks is a largely interdisciplinary topic. It exploits cross-fertilization among different scientific areas, like physics of complex systems, epidemiology, and microbiology. The SIR and SIS dynamics interact in the spreading mechanism, like in real life This model captures most of the relevant mechanisms of epidemic spreading, in a schematic way. Hosts follow SIR evolution, while vectors are governed by SIS dynamics This is inspired by the idea of two species with very different life expectancies. Virulence/chronicity parameter p = 1/(1 +eH/vV) prophylaxis/vaccination parameter h = 1/(1 +vH/eV) linear size of the model time needed for the infection to reach the lattice boundary order parameter defined as 1 if a realization of the infection reaches the lattice boundary and 0 otherwise total number of recovered hosts when the infection stops. Binder cumulant - like combination, useful to identify the critical line various critical exponents governing the universal behavior Their theoretical values in the dynamical percolation class are: β
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