Severe population collapses and species extinctions in multi-host epidemic dynamics

Most infectious diseases including more than half of known human pathogens are not restricted to just one host, yet much of the mathematical modeling of infections has been limited to a single species. We investigate consequences of a single epidemic propagating in multiple species and compare and contrast it with the endemic steady state of the disease. We use the two-species Susceptible-Infected-Recovered (SIR) model to calculate the severity of post-epidemic collapses in populations of two host species as a function of their initial population sizes, the times individuals remain infectious, and the matrix of infection rates. We derive the criteria for a very large, extinction-level, population collapse in one or both of the species. The main conclusion of our study is that a single epidemic could drive a species with high mortality rate to local or even global extinction provided that it is co-infected with an abundant species. Such collapse-driven extinctions depend on factors different than those in the endemic steady state of the disease

Evolutionary dynamics of the most populated genotype on rugged fitness landscapes

We consider an asexual population evolving on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local optima. We track the most populated genotype as it changes when the population jumps from a fitness peak to a better one during the process of adaptation. This is done using the dynamics of the shell model which is a simplified version of the quasispecies model for infinite populations and standard Wright-Fisher dynamics for large finite populations. We show that the population fraction of a genotype obtained within the quasispecies model and the shell model match for fit genotypes and at short times, but the dynamics of the two models are identical for questions related to the most populated genotype. We calculate exactly several properties of the jumps in infinite populations some of which were obtained numerically in previous works. We also present our preliminary simulation results for finite populations. In particular, we measure the jump distribution in time and find that it decays as $t^{-2}$ as in the quasispecies problem.Comment: Minor changes. To appear in Phys Rev

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a {\it quasispecies} which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.Comment: Proceedings of Statphys conference at IIT Guwahati, to be published in Praman

Quantum tight-binding chains with dissipative coupling

We present a one-dimensional tight-binding chain of two-level systems coupled only through common dissipative Markovian reservoirs. This quantum chain can demonstrate anomalous thermodynamic behavior contradicting Fourier law. Population dynamics of individual systems of the chain is polynomial with the order determined by the initial state of the chain. The chain can simulate classically hard problems, such as multi-dimensional random walks

Inertial game dynamics and applications to constrained optimization

Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied "heavy ball with friction" optimization method. By exploiting a well-known link between the replicator dynamics and the Shahshahani geometry on the space of mixed strategies, the dynamics are stated in a Riemannian geometric framework where trajectories are accelerated by the players' unilateral payoff gradients and they slow down near Nash equilibria. Surprisingly (and in stark contrast to another second-order variant of the replicator dynamics), the inertial replicator dynamics are not well-posed; on the other hand, it is possible to obtain a well-posed system by endowing the mixed strategy space with a different Hessian-Riemannian (HR) metric structure, and we characterize those HR geometries that do so. In the single-agent version of the dynamics (corresponding to constrained optimization over simplex-like objects), we show that regular maximum points of smooth functions attract all nearby solution orbits with low initial speed. More generally, we establish an inertial variant of the so-called "folk theorem" of evolutionary game theory and we show that strict equilibria are attracting in asymmetric (multi-population) games - provided of course that the dynamics are well-posed. A similar asymptotic stability result is obtained for evolutionarily stable strategies in symmetric (single- population) games.Comment: 30 pages, 4 figures; significantly revised paper structure and added new material on Euclidean embeddings and evolutionarily stable strategie

An Analysis on Selection for High-Resolution Approximations in Many-Objective Optimization

This work studies the behavior of three elitist multi- and many-objective evolutionary algorithms generating a high-resolution approximation of the Pareto optimal set. Several search-assessment indicators are defined to trace the dynamics of survival selection and measure the ability to simultaneously keep optimal solutions and discover new ones under different population sizes, set as a fraction of the size of the Pareto optimal set.Comment: apperas in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Mathematical Modelling of Mosquito Dispersal in a Heterogeneous Environment.

Mosquito dispersal is a key behavioural factor that affects the persistence and resurgence of several vector-borne diseases. Spatial heterogeneity of mosquito resources, such as hosts and breeding sites, affects mosquito dispersal behaviour and consequently affects mosquito population structures, human exposure to vectors, and the ability to control disease transmission. In this paper, we develop and simulate a discrete-space continuous-time mathematical model to investigate the impact of dispersal and heterogeneous distribution of resources on the distribution and dynamics of mosquito populations. We build an ordinary differential equation model of the mosquito life cycle and replicate it across a hexagonal grid (multi-patch system) that represents two-dimensional space. We use the model to estimate mosquito dispersal distances and to evaluate the effect of spatial repellents as a vector control strategy. We find evidence of association between heterogeneity, dispersal, spatial distribution of resources, and mosquito population dynamics. Random distribution of repellents reduces the distance moved by mosquitoes, offering a promising strategy for disease control