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

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

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

A mass-structured individual-based model of the chemostat: convergence and simulation

We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting on the bacteria are explicitly described (growth, division and up-take). Bacteria interact via consumption. We set the exact Monte Carlo simulation algorithm of this model and its mathematical representation as a stochastic process. We prove the convergence of this process to the solution of an integro-differential equation when the population size tends to infinity. Finally, we propose several numerical simulations