Traveling Waves of a Mutualistic Model of Mistletoes and Birds

The existences of an asymptotic spreading speed and traveling wave solutions for a diffusive model which describes the interaction of mistletoe and bird populations with nonlocal diffusion and delay effect are proved by using monotone semiflow theory. The effects of different dispersal kernels on the asymptotic spreading speeds are investigated through concrete examples and simulations

Modelling Wolbachia Infection in a Sex-Structured Mosquito Population Carrying West Nile Virus

Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number R0 is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced

Stability of traveling wave solutions for a nonlocal Lotka-Volterra model

In this paper, we studied the stability of traveling wave solutions of a two-species Lotka-Volterra competition model in the form of a coupled system of reaction diffusion equations with nonlocal intraspecific and interspecific competitions in space at times. First, the uniform upper bounds for the solutions of the model was proved. By using the anti-weighted method and the energy estimates, the asymptotic stability of traveling waves with large wave speeds of the system was established

Forecasting Natural Regeneration of Sagebrush After Wildfires Using Population Models and Spatial Matching

Context Addressing ecosystem degradation in the Anthropocene will require ecological restoration across large spatial extents. Identifying areas where natural regeneration will occur without direct resource investment will improve scalability of restoration actions. Objectives An ecoregion in need of large scale restoration is the Great Basin of the Western US, where increasingly large and frequent wildfires threaten ecosystem integrity and its foundational shrub species. We develop a framework to forecast where postwildfire regeneration of sagebrush cover (Artemisia spp.) is likely to occur within the burnt areas across the region (\u3e900,000 km2). Methods First, we parameterized population models using Landsat satellite-derived time series of sagebrush cover. Second, we evaluated the out-of-sample performance by predicting natural regeneration in wildfres not used for model training. This model assessment reproduces a management-oriented scenario: making restoration decisions shortly after wildfires with minimal local information. Third, we asked how accounting for increasingly fine-scale spatial heterogeneity could improve model forecasting accuracy. Results Regional-level models revealed that sagebrush post-fire recovery is slow, estimating \u3e 80-year time horizon to reach an average cover at equilibrium of 16.6% (CI95% 9–25). Accounting for wildfre and within-wildfre spatial heterogeneity improved out-ofsample forecasts, resulting in a mean absolute error of 3.5 ± 4.3% cover, compared to the regional model with an error of 7.2 ± 5.1% cover. Conclusions We demonstrate that combining population models and non-parametric spatial matching provides a fexible framework for forecasting plant population recovery. Models for population recovery applied to Landsat-derived time series will assist restoration decision-making, including identifying priority targets for restoration

An Age-structured Model of Bird Migration

An approach to modelling bird migration is proposed, in which there is a region where birds do not move but spend time breeding. Birds leave this breeding region and enter a migration flyway which is effectively a one-way corridor starting and ending at the breeding location. Mathematically, the flyway is a curve parametrised by arc-length. Flight speed depends on position along the flyway, to take account of factors such as wind and the pausing of birds at various locations for wintering or stopovers. Per-capita mortality along the flyway is both position and age-dependent, allowing for increased risks at stopover locations due to predation, and increased risks to immature birds. A reaction-advection age-structured equation models population dynamics along the flyway and, using a Laplace transform technique, the model is reduced to a scalar delay differential equation for the number of adult birds at the breeding location. Extinction and persistence criteria are obtained for the bird population and the results of computer simulations are presented

Multiple Dose Pharmacokinetic Models Predict Bioavailability of Toxins in Vertebrate Herbivores

In this paper, compartmental pharmacokinetic models are built to predict the concentration of toxic phytochemical in the gastrointestinal tract and blood following oral intake by an individual vertebrate herbivore. The existing single and multiple dose pharmacokinetic models are extended by inclusion of impulsive differential equations which account for an excretion factor whereby unchanged toxins are excreted in the feces due to gastrointestinal mobility. An index α is defined to measure the fraction of bioavailability attributed to the excretion factor of gastrointestinal motility. Sensitivity analysis was conducted and suggests, for any toxin, the bioavailability index α depends mostly on absorption rate of toxin from gastrointestinal tract into the blood, frequency of elimination due to gastrointestinal motility, and the frequency of toxin intake, under the model assumptions

Some Vector Borne Diseases With Structured Host Populations: Extinction and Spatial Spread

We derive from a structured population model a system of delay differential equations describing the interaction of five subpopulations, namely susceptible and infected adult and juvenile reservoirs and infected adult vectors, for a vector borne disease with particular reference to West Nile virus, and we also incorporate spatial movements by considering the analogue reaction diffusion systems with nonlocal delayed terms. Specific conditions for the disease eradication and sharp conditions for the local stability of the disease-free equilibrium are obtained using comparison techniques coupled with the spectral theory of monotone linear semi flows. A formal calculation of the minimal wave speed for the traveling waves is given and compared with field observation data.</p