Intermittent Precipitation-Dependent Interactions, Encompassing Allee Effect, May Yield Vegetation Patterns in a Transitional Parameter Range.

We construct a spatial model that incorporates Allee-type and competition interactions for vegetation as an evolving random field of biomass density. The cumulative effect of close-range precipitation-dependent interactions is controlled by a parameter defining precipitation frequency. We identify a narrow parameter range in which the behavior of the system changes from survival of vegetation to extinction, via a transitional aggregation pattern.

Epidemic highs and lows: a stochastic diffusion model for active cases.

We derive a stochastic epidemic model for the evolving density of infective individuals in a large population. Data shows main features of a typical epidemic consist of low periods interspersed with outbreaks of various intensities and duration. In our stochastic differential model, a novel reproductive term combines a factor expressing the recent notion of 'attenuated Allee effect' and a capacity factor is controlling the size of the process.

Allee Effects Plus Noise Induce Population Dynamics Resembling Binary Markov Highs and Lows.

We show that the combination of Allee effects and noise can produce a stochastic process with alternating sudden decline to a low population phase, followed, after a random time, by abrupt increase in population density. We introduce a new, flexible, deterministic model of attenuated Allee effects, which interpolates between the logistic and a usual Allee model. Into this model, we incorporate environmental and demographic noise.

A stochastic model for water-vegetation systems and the effect of decreasing precipitation on semi-arid environments.

Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming part of these regions into deserts in some cases. Although it is documented that a decreasing tendency in precipitation might induce earlier disappearance of vegetation, quantifying the relationship between decrease of precipitation and vegetation endurance remains a challenging task due to the inherent complexities involved in distinct scenarios.

Modeling ephemeral mating encounters in insects: The emergence of mate-finding Allee effects and applications to theoretical models of sterile release.

Lack of successful mating encounters in two-sex insect populations is a mechanism that might trigger reproductive Allee effects. In this paper I examine a function that models ephemeral mating encounters through the expected density of pairs formed by individuals of both sexes at any time. When this function is incorporated in a general system of differential equations for a two-sex population the solutions exhibit the emergence of an Allee effect for low population densities.

A Model for Mountain Pine Beetle Outbreaks in an Age-Structured Forest: Predicting Severity and Outbreak-Recovery Cycle Period.

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations.

Pest persistence and eradication conditions in a deterministic model for sterile insect release.

The release of sterile insects is an environment friendly pest control method used in integrated pest management programmes. Difference or differential equations based on Knipling's model often provide satisfactory qualitative descriptions of pest populations subject to sterile release at relatively high densities with large mating encounter rates, but fail otherwise. In this paper, I derive and explore numerically deterministic population models that include sterile release together with scarce mating encounters in the particular case of species with long lifespan and multiple matings.

Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population.

To determine optimal sterile insect release policies in area-wide integrated pest management is a challenge that users of this pest control method inevitably confront. In this note we provide approximations to best policies of release through the use of simulated annealing. The discrete time model for the population dynamics includes the effects of sterile insect release and density dependence in the pest population.

A model for the transmission dynamics of Orientia tsutsugamushi among its natural reservoirs.

The bacteria Orientia tsutsugamushi is the causative agent of scrub typhus, a prevalent disease in Asian countries that can affect humans and which shows an alarming increase of cases during the last years, especially in rural areas. Unfortunately, there is no vaccine for scrub typhus, and antibiotic treatments successfully used in the past appear to be inefficient to treat some strains of O. tsutsugamushi.

The effect of patterns of infectiousness on epidemic size.

In the course of an infectious disease in a population, each infected individual presents a different pattern of progress through the disease, producing a corresponding pattern of infectiousness. We postulate a stochastic infectiousness process for each individual with an almost surely finite integral, or total infectiousness. Individuals also have different contact rates.

Screening Two Lycopersicon peruvianum Collections for Resistance to Tomato spotted wilt virus.

The United States Department of Agriculture (USDA) Research Service and the Tomato Genetics Resource Center (TGRC) Lycopersicon peruvianum germplasm collections (16,335 plants from 285 accessions) were screened with the Tomato spotted wilt virus (TSWV) isolates TSWV6 from Hawaii, and An-1 from Western Australia. Using TSWV6 to screen for resistance, 10,634 L. peruvianum plants from 280 accessions were screened for resistance, resulting in 168 (60%) accessions with 1,437 (14%) plants indicating resistance, with all 1,404 89S (Sw-5+/Sw-5+) and 1,456 89R (Sw-5/Sw-5) controls infected.

Bimodal epidemic size distributions for near-critical SIR with vaccination.

We introduce a recursive algorithm which enables the computation of the distribution of epidemic size in a stochastic SIR model for very large population sizes. In the important parameter region where the model is just slightly supercritical, the distribution of epidemic size is decidedly bimodal. We find close agreement between the distribution for large populations and the limiting case where the distribution is that of the time a Brownian motion hits a quadratic curve.

Sustained oscillations via coherence resonance in SIR.

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation.