Fisher Waves: an individual based stochastic model

The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov (SFKPP) equation. We derive here an individual based, stochastic model founded on the spatial Moran process where fluctuations are treated exactly. At high selection pressure, the results of this model are different from the classical FKPP. At small selection pressure, the front behavior can be mapped into a Brownian motion with drift, the properties of which can be derived from microscopic parameters of the Moran model. Finally, we show that the diffusion coefficient and the noise amplitude of SFKPP are not independent parameters but are both determined by the dispersal kernel of individuals

An Individual-based Probabilistic Model for Fish Stock Simulation

We define an individual-based probabilistic model of a sole (Solea solea) behaviour. The individual model is given in terms of an Extended Probabilistic Discrete Timed Automaton (EPDTA), a new formalism that is introduced in the paper and that is shown to be interpretable as a Markov decision process. A given EPDTA model can be probabilistically model-checked by giving a suitable translation into syntax accepted by existing model-checkers. In order to simulate the dynamics of a given population of soles in different environmental scenarios, an agent-based simulation environment is defined in which each agent implements the behaviour of the given EPDTA model. By varying the probabilities and the characteristic functions embedded in the EPDTA model it is possible to represent different scenarios and to tune the model itself by comparing the results of the simulations with real data about the sole stock in the North Adriatic sea, available from the recent project SoleMon. The simulator is presented and made available for its adaptation to other species.Comment: In Proceedings AMCA-POP 2010, arXiv:1008.314

Individual-based lattice model for spatial spread of epidemics

We present a lattice gas cellular automaton (LGCA) to study spatial and temporal dynamics of an epidemic of SIR (susceptible-infected-removed) type. The automaton is fully discrete, i.e. space, time and number of individuals are discrete variables. The automaton can be applied to study spread of epidemics in both human and animal populations. We investigate effects of spatial inhomogeneities in initial distribution of infected and vaccinated populations on the dynamics of epidemic of SIR type. We discuss vaccination strategies which differ only in spatial distribution of vaccinated individuals. Also, we derive an approximate, mean-field type description of the automaton, and discuss differences between the mean-field dynamics and the results of LGCA simulation.Comment: 13 pages, 5 figure

Community-driven dispersal in an individual-based predator-prey model

We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefined tolerance threshold. The spatiotemporal dynamics of the model is described in terms of this threshold. We compare this dynamics with the one obtained through density-independent dispersal and find marked differences. In the community-driven scenario, the spatial correlations in the population density do not vary in a linear fashion as we increase the tolerance threshold. Instead we find the system to cross different dynamical regimes as the threshold is raised. Spatial patterns evolve from disordered, to scale-free complex patterns, to finally becoming well-organized domains. This model therefore predicts that natural populations, the dispersal strategies of which are likely to be influenced by their local environment, might be subject to complex spatiotemporal dynamics.Comment: 43 pages, 7 figures, vocabulary modifications, discussion expanded, references added, Ecological Complexity accepte

Outlook for tuberculosis elimination in California: An individual-based stochastic model.

RationaleAs part of the End TB Strategy, the World Health Organization calls for low-tuberculosis (TB) incidence settings to achieve pre-elimination (<10 cases per million) and elimination (<1 case per million) by 2035 and 2050, respectively. These targets require testing and treatment for latent tuberculosis infection (LTBI).ObjectivesTo estimate the ability and costs of testing and treatment for LTBI to reach pre-elimination and elimination targets in California.MethodsWe created an individual-based epidemic model of TB, calibrated to historical cases. We evaluated the effects of increased testing (QuantiFERON-TB Gold) and treatment (three months of isoniazid and rifapentine). We analyzed four test and treat targeting strategies: (1) individuals with medical risk factors (MRF), (2) non-USB, (3) both non-USB and MRF, and (4) all Californians. For each strategy, we estimated the effects of increasing test and treat by a factor of 2, 4, or 10 from the base case. We estimated the number of TB cases occurring and prevented, and net and incremental costs from 2017 to 2065 in 2015 U.S. dollars. Efficacy, costs, adverse events, and treatment dropout were estimated from published data. We estimated the cost per case averted and per quality-adjusted life year (QALY) gained.Measurements and main resultsIn the base case, 106,000 TB cases are predicted to 2065. Pre-elimination was achieved by 2065 in three scenarios: a 10-fold increase in the non-USB and persons with MRF (by 2052), and 4- or 10-fold increase in all Californians (by 2058 and 2035, respectively). TB elimination was not achieved by any intervention scenario. The most aggressive strategy, 10-fold in all Californians, achieved a case rate of 8 (95% UI 4-16) per million by 2050. Of scenarios that reached pre-elimination, the incremental net cost was $20 billion (non-USB and MRF) to$48 billion. These had an incremental cost per QALY of $657,000 to$3.1 million. A more efficient but somewhat less effective single-lifetime test strategy reached as low as $80,000 per QALY.ConclusionsSubstantial gains can be made in TB control in coming years by scaling-up current testing and treatment in non-USB and those with medical risks

A spatially explicit Markovian individual-based model for terrestrial plant dynamics

An individual-based model (IBM) of a spatiotemporal terrestrial ecological population is proposed. This model is spatially explicit and features the position of each individual together with another characteristic, such as the size of the individual, which evolves according to a given stochastic model. The population is locally regulated through an explicit competition kernel. The IBM is represented as a measure-valued branching/diffusing stochastic process. The approach allows (i) to describe the associated Monte Carlo simulation and (ii) to analyze the limit process under large initial population size asymptotic. The limit macroscopic model is a deterministic integro-differential equation.Comment: 31 pages, 1 figur