arXiv subjects
Publications and source records attributed to Rinaldo B. Schinazi.
We consider a stochastic model for an evolving population. We show that in the presence of genotype extinctions the population dies out for a low mutation probability but may survive for a high mutation probability. This turns upside down the widely held belief that above a certain mutation threshold a population cannot survive.
Many species live in colonies that prosper for a while and then collapse. After the collapse the colony survivors disperse randomly and found new colonies that may or may not make it depending on the new environment they find. We use birth and death chains in random environments to model such a population and to argue that random dispersion is a superior strategy for survival.
The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the distribution of the waiting time for a second mutation. This models the time of appearance of the first cancerous cell in a tissue. Our model is an alternative to the Moran model with mutations.
We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate over the death rate at a site converges to some limit as the site goes to infinity. We show that the existence of a phase transition depends critically on the value of this limit.
It has long been known that antibiotic treatment will not completely kill off a bacteria population. For many species a small fraction of bacteria is not sensitive to antibiotics. These bacteria are said to persist. Recently it has been shown that persistence is not a permanent state and that in fact a bacterium can switch back and forth between persistent and non persistent states. We introduce two stochastic models for bacteria persistence. In both models there are mass killings of non persistent bacteria at certain times. The first model has deterministic killing times and the second one has random killing times. Both models suggest that persistence may be a successful strategy for a wide range of parameter values.
We consider an interacting particle system representing the spread of a rumor by agents on the $d$-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate λ. At rate αa spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.
Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best adapted genotype, leading to a population composed of low replicating mutants that is eventually doomed. We propose a new branching model that shows that this is not necessarily so. That is, a population composed of ever changing mutants may survive.
We consider a stochastic model for species evolution. A new species is born at rate lambda and a species dies at rate mu. A random number, sampled from a given distribution F, is associated with each new species at the time of birth. Every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time of a species with a given fitness f. We show that the survival time distribution depends crucially on whether f f_c where f_c is a critical fitness that is computed explicitly.
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type that is killed is the one with the smallest fitness. We show that there is a sharp phase transition when the birth probability is larger than the death probability. The set of species with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the critical disappear after a finite (random) time.
We use spatial and non spatial models to argue that competition alone may explain why two influenza strains do not usually coexist. The more virulent strain is likely to crowd out the less virulent one. This can be seen as a consequence of the Exclusion Principle of Ecology. We exhibit, however, a spatial model for which coexistence is possible.
We propose a simple model to compute the probability of success under a quorum sensing strategy. We show that a quorum sensing strategy has a higher probability of success than an individualistic strategy when, for instance, the probability of success for a single individual is low and the cost of building a quorum is not too high. On the other hand if the cost of building a quorum is too high then the probability of success under quorum sensing always decreases as a function of the quorum.
We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an application we show that a type of weak coexistence is possible in the nearest-neighbor ``grass-bushes-trees'' successional model introduced in Durrett and Swindle (1991).
We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the $d$-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside of this interval.
We propose a one mutation model for cancer with a mutation rate that increases with time. Under rather general hypotheses the number of mutations is necessarily a (non homogeneous) Poisson process with the prescribed mutation rate. We show that the cumulative probability of cancer up to time $t$ is, up to a multiplicative constant, an antiderivative of the mutation rate.
We propose two simple probability models to compute the probability of an influenza pandemic. Under a random walk model the probability that all pandemics between times 0 and 300 occur by time 150 is 1/2. Under a Poisson model with mean inter arrival time of 30 years the probability that no pandemic occurs during at least 60 years is 14%. These probabilities are much higher than generally perceived. So yes the next influenza pandemic will happen but maybe much later than generally thought.
Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $λ$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a mutation occurs, and the new pathogen has a different type from all previously observed pathogens. When a new type appears in the population, it survives for an exponential amount of time with mean 1, independently of all the other types. All pathogens of that type are killed simultaneously. Schinazi and Schweinsberg (2006) have shown that this model on $\Z^d$ behaves rather differently from its non-spatial version. In this paper, we show that this model on a homogeneous tree captures features from both the non-spatial version and the $\Z^d$ version. We also obtain comparison results between this model and the basic contact process on general graphs.
We introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate ϕuntil the maximum of N individuals has been reached at the site. Once the flock reaches N individuals, then, and only then, it starts giving birth on each of the 2d neighboring sites at rate λ(N). Finally, disaster strikes at rate 1, that is, the whole flock disappears. Our model shows that, at least in theory, there is a critical maximum flock size above which a species is certain to disappear and below which it may survive.