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. The aggregation pattern is tied to the initial configuration and appears to arise differently from Turing's diffusion and differential flow patterns of other models. There is close agreement of our critical transition parameter range with that of the corresponding evolving random mean-field model.

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. Simulation of this model produces sample paths of the stochastic density of infectives, which behave much like long-time Covid-19 case data of recent years. Writing the process as a stochastic diffusion allows us to derive its stationary distribution, showing the relative time spent in low levels and in outbursts. Much of the behaviour of the density of infectives can be understood in terms of the interacting drift and diffusion coefficient processes, or, alternatively, in terms of the balance between noise level and the attenuation parameter of the Allee effect. Unexpected results involve the effect of increasing overall noise variance on the density of infectives, in particular on its level-crossing function.

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. The solution of the resulting Kolmogorov forward equation shows a dichotomous distribution of residence times with heavy occupation of high, near saturation, and low population states. Investigation of simulated sample paths reveals that indeed attenuated Allee effects and noise, acting together, produce alternating, sustained, low and high population levels. We find that the transition times between the two types of states are approximately exponentially distributed, with different parameters, rendering the embedded hi-low process approximately Markov.

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. In this paper we present a model for precipitation-vegetation dynamics in semi-arid landscapes that can be used to explore numerically the impact of decreasing precipitation trends on appearance of desertification events. The model, a stochastic differential equation approximation derived from a Markov jump process, is used to generate extensive simulations that suggest a relationship between precipitation reduction and the desertification process, which might take several years in some instances.

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. Compared with current conceptual models for mate-finding Allee effects, the proposed pairing function does not include a parameter that quantifies the Allee effect strength, a feature that might be useful when information to parameterize Allee effects is unavailable. The mating function is then used to numerically explore how mate-finding Allee effects are enhanced by the release of sterile males in theoretical models where (i) the initial sex ratio is skewed, (ii) sterile males are released in pulses and (iii) partial female remating is allowed.

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. Stability of fixed points is analyzed as a function of (thermally controlled) MPB population growth rates and indicates the existence of periodic outbreaks that intensify as growth rates increase. We devise analytical methods to predict outbreak severity and duration as well as outbreak return time. After incorporating a spatial aspect and controlling initial stand demographic variation, the model predicts cycle periods that fall within observed outbreak return time ranges. To assess future MPB impact on forests, we use climate model projected temperatures with our model-based approximation methods to predict potential severity of future outbreaks that reflect the effects of changing climate.

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. The differential equations account separately the effects of mating failure due to sterile male release and the frequency of mating encounters. When insects spatial spread is incorporated through diffusion terms, computations reveal the possibility of steady pest persistence in finite size patches. In the presence of density dependence regulation, it is observed that sterile release might contribute to induce sudden suppression of the pest population.

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. Spatial movement is introduced through integrodifference equations, which allow the use of the stochastic search in cases where movement is described through arbitrary dispersal kernels. As a byproduct of the computations, an assessment of appropriate control zone sizes is possible.

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. We introduce a mathematical model that approximates the dynamics of the bacteria among its natural reservoirs. After computing the basic reproductive number from the proposed model, we explore its sensitivity to the parameter values that may be affected by application of control measures. This theoretical model may be of interest to pest managers as well as health authorities interested in gaining insight into the public management of the disease, through a better understanding of its qualitative dynamics.

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. We show that the distribution of the final epidemic size depends only on the contact rates and the integrated infectiousness. As a particular case, zero infectiousness on an initial time interval corresponds to a period of latency, which does not affect the final epidemic size in general stochastic and deterministic epidemic models, as is well known from the literature.

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 Anwa-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. When using Anwa-1 for screening, 864 (15%) of 5,701 L. peruvianum plants were uninfected from 106 of the 181 accessions tested, and 472 (95%) of the 495 89S and 421 (73%) of the 574 89R controls were infected. Of the 172 accessions tested with both isolates, 54 were resistant to one isolate but not the other. Additionally, more accessions from the USDA than from the TGRC collection indicated resistance. TSWV-resistant accessions were somewhat equally distributed throughout the L. peruvianum geographic range, with an observation that northern Chile and southern Peru seemed to have an unusually high portion of accession indicating resistance. The value of Sw-5 is discussed in relationship to potential additional sources of TSWV resistance.

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. The model includes the possibility of vaccination during the epidemic. The effects of the parameters, including vaccination level, on the form of the epidemic size distribution are explored.

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. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon.