An Analysis of the Coexistence of Three Competing Species with a Shared Pathogen

We consider an SI model of three competing species that are all affected by a single pathogen which is transmitted directly via mass action. The total population sizes of the three species satisfy a three-dimensional Lotka-Volterra competition model. We address the interaction between competition and disease dynamics, and show that infected coexistence in the model is determined by the values of the basic reproduction numbers as well as the relative strengths of intra-specific crowding versus inter-specific competition for all three species.Keywords: Lotka-Volterra Competition, three-species coexistence, SI mass-action model, basic reproduction numbe

High-Order Staggered Finite Difference Methods for Maxwell's Equations in Dispersive Media

We study the stability properties of, and the phase error present in, several higher order (in space) staggered finite difference schemes for Maxwell's equations coupled with a Debye or Lorentz polarization model. We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the first order spatial derivative operator. This alternative representation allows the derivation of a concise formula for the numerical dispersion relation for all (even) order schemes applied to each model, including the limiting (infinite order) case. We further derive a closed-form analytical stability condition for these schemes as a function of the order of the method. Using representative numerical values for the physical parameters, we validate the stability criterion while quantifying numerical dissipation. Lastly, we demonstrate the effect that the spatial discretization order, and the corresponding stability constraint, has on the dispersion error.Keywords: Maxwell’s Equations, Debye, Lorentz, higher order FDTD, dissipation, dispersion, phase error

Modelling Vector Transmission and Epidemiology of Co-Infecting Plant Viruses.

Co-infection of plant hosts by two or more viruses is common in agricultural crops and natural plant communities. A variety of models have been used to investigate the dynamics of co-infection which track only the disease status of infected and co-infected plants, and which do not explicitly track the density of inoculative vectors. Much less attention has been paid to the role of vector transmission in co-infection, that is, acquisition and inoculation and their synergistic and antagonistic interactions. In this investigation, a general epidemiological model is formulated for one vector species and one plant species with potential co-infection in the host plant by two viruses. The basic reproduction number provides conditions for successful invasion of a single virus. We derive a new invasion threshold which provides conditions for successful invasion of a second virus. These two thresholds highlight some key epidemiological parameters important in vector transmission. To illustrate the flexibility of our model, we examine numerically two special cases of viral invasion. In the first case, one virus species depends on an autonomous virus for its successful transmission and in the second case, both viruses are unable to invade alone but can co-infect the host plant when prevalence is high

Coupled transport and reaction kinetics control the nitrate source-sink function of hyporheic zones

The fate of biologically available nitrogen (N) and carbon (C) in stream ecosystems is controlled by the coupling of physical transport and biogeochemical reaction kinetics. However, determining the relative role of physical and biogeochemical controls at different temporal and spatial scales is difficult. The hyporheic zone (HZ), where groundwater–stream water mix, can be an important location controlling N and C transformations because it creates strong gradients in both the physical and biogeochemical conditions that control redox biogeochemistry. We evaluated the coupling of physical transport and biogeochemical redox reactions by linking an advection, dispersion, and residence time model with a multiple Monod kinetics model simulating the concentrations of oxygen (O₂), ammonium (NH₄), nitrate (NO₃), and dissolved organic carbon (DOC). We used global Monte Carlo sensitivity analyses with a nondimensional form of the model to examine coupled nitrification-denitrification dynamics across many scales of transport and reaction conditions. Results demonstrated that the residence time of water in the HZ and the uptake rate of O₂ from either respiration and/or nitrification determined whether the HZ was a source or a sink of NO₃ to the stream. We further show that whether the HZ is a net NO₃ source or net NO₃ sink is determined by the ratio of the characteristic transport time to the characteristic reaction time of O₂ (i.e., the Damköhler number, Da[subscript O2]), where HZs with Da[subscript O2] < 1 will be net nitrification environments and HZs with Da[subscript O2] ≪ 1 will be net denitrification environments. Our coupling of the hydrologic and biogeochemical limitations of N transformations across different temporal and spatial scales within the HZ allows us to explain the widely contrasting results of previous investigations of HZ N dynamics which variously identify the HZ as either a net source or sink of NO₃. Our model results suggest that only estimates of residence times and O₂ uptake rates are necessary to predict this nitrification-denitrification threshold and, ultimately, whether a HZ will be either a net source or sink of NO₃

Coinfections by noninteracting pathogens are not independent and require new tests of interaction.

If pathogen species, strains, or clones do not interact, intuition suggests the proportion of coinfected hosts should be the product of the individual prevalences. Independence consequently underpins the wide range of methods for detecting pathogen interactions from cross-sectional survey data. However, the very simplest of epidemiological models challenge the underlying assumption of statistical independence. Even if pathogens do not interact, death of coinfected hosts causes net prevalences of individual pathogens to decrease simultaneously. The induced positive correlation between prevalences means the proportion of coinfected hosts is expected to be higher than multiplication would suggest. By modelling the dynamics of multiple noninteracting pathogens causing chronic infections, we develop a pair of novel tests of interaction that properly account for nonindependence between pathogens causing lifelong infection. Our tests allow us to reinterpret data from previous studies including pathogens of humans, plants, and animals. Our work demonstrates how methods to identify interactions between pathogens can be updated using simple epidemic models

Modelling Vector Transmission and Epidemiology of Co-Infecting Plant Viruses.

Co-infection of plant hosts by two or more viruses is common in agricultural crops and natural plant communities. A variety of models have been used to investigate the dynamics of co-infection which track only the disease status of infected and co-infected plants, and which do not explicitly track the density of inoculative vectors. Much less attention has been paid to the role of vector transmission in co-infection, that is, acquisition and inoculation and their synergistic and antagonistic interactions. In this investigation, a general epidemiological model is formulated for one vector species and one plant species with potential co-infection in the host plant by two viruses. The basic reproduction number provides conditions for successful invasion of a single virus. We derive a new invasion threshold which provides conditions for successful invasion of a second virus. These two thresholds highlight some key epidemiological parameters important in vector transmission. To illustrate the flexibility of our model, we examine numerically two special cases of viral invasion. In the first case, one virus species depends on an autonomous virus for its successful transmission and in the second case, both viruses are unable to invade alone but can co-infect the host plant when prevalence is high

Coinfections by noninteracting pathogens are not independent and require new tests of interaction.

If pathogen species, strains, or clones do not interact, intuition suggests the proportion of coinfected hosts should be the product of the individual prevalences. Independence consequently underpins the wide range of methods for detecting pathogen interactions from cross-sectional survey data. However, the very simplest of epidemiological models challenge the underlying assumption of statistical independence. Even if pathogens do not interact, death of coinfected hosts causes net prevalences of individual pathogens to decrease simultaneously. The induced positive correlation between prevalences means the proportion of coinfected hosts is expected to be higher than multiplication would suggest. By modelling the dynamics of multiple noninteracting pathogens causing chronic infections, we develop a pair of novel tests of interaction that properly account for nonindependence between pathogens causing lifelong infection. Our tests allow us to reinterpret data from previous studies including pathogens of humans, plants, and animals. Our work demonstrates how methods to identify interactions between pathogens can be updated using simple epidemic models