Invasion dynamics of epidemic with the Allee effect

Investigating the likely success of epidemic invasion is important in the epidemic management and control. In the present study, the invasion of epidemic is initially introduced to a predator-prey system, both species of which are considered to be subject to the Allee effect. Mathematically, the invasion dynamics is described by three nonlinear diffusion-reaction equations and the spatial implicit and explicit models are designed. By means of extensive numerical simulations, the results of spatial implicit model show that the Allee effect has an opposite impact on the invasion criteria and local dynamics when that on the different species. As the intensity of the Allee effect increases, the domain of epidemic invasion reduces and the system dynamics is changed from the stable state to the limit cycle and finally becomes the chaotic state when the susceptible prey with the Allee effect, but the domain expands and the system dynamics is changed from limit cycle to a table point when the predator is subject to the Allee effect. Results from the spatial explicit model show that the strong intensity of the Allee effect can lead to the catastrophic global extinction of all species in the case of that on the susceptible prey. While the predator with the Allee effect, the increased intensity of which makes spatial species reach a stable state. Furthermore, numerical simulations reveal a certain relationship between the invasion speed and spatial patterns.     

Nature’s care: diarrhea, watershed protection, and biodiversity conservation in Flores, Indonesia

Part of the puzzle surrounding biodiversity loss lies in an incomplete understanding of how humans value the functions and services that flow from biodiversity conservation projects. This paper takes a closer look at the links between the conservation of biodiversity and the livelihoods of rural people who live on the fringes of the parks and protected areas. We revisit some of the key aspects of ecosystem valuation—purpose, methodology, and policy design and implementation—because the links between biodiversity conservation, ecosystem services, and human welfare are obscured by considerable smoke and mirrors. Using a biodiversity conservation project (Ruteng Park) on Flores Island in Indonesia as a case study, we build a concrete empirical example of ecosystem valuation. This conservation project has resulted in spatially patchy watershed protection that allows us to identify and estimate the impacts of watershed services on human health (diarrhea prevalence) in the buffer zone of the park. We conclude by offering a plan of research to improve the design of conservation interventions for protecting biodiversity and providing ecosystem services. These recommendations include developing more conceptual knowledge on the linkages between biodiversity and ecosystem services; scaling up valuation efforts of underappreciated services such as health; shifting focus from valuing services individually to valuing multiple benefits from the same area; and conducting conservation policy experiments to identify causal outcomes (including defensible estimates of ecosystem values).

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata, we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively, habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility of using human disturbance in habitat as a potential epidemic-control method in conservation.     

Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito

We present a stochastic dynamical model for the transmission of dengue that takes into account seasonal and spatial dynamics of the vector Aedes aegypti. It describes disease dynamics triggered by the arrival of infected people in a city. We show that the probability of an epidemic outbreak depends on seasonal variation in temperature and on the availability of breeding sites. We also show that the arrival date of an infected human in a susceptible population dramatically affects the distribution of the final size of epidemics and that early outbreaks have a low probability. However, early outbreaks are likely to produce large epidemics because they have a longer time to evolve before the winter extinction of vectors. Our model could be used to estimate the risk and final size of epidemic outbreaks in regions with seasonal climatic variations.     

The role of transmissible diseases in the Holling-Tanner predator-prey model

Transmissible diseases are known to induce remarkable major behavioral changes in predator-prey systems. However, little attention has been paid to model such situations. The latter would allow to predict useful applications in both dynamics and control. Here the Holling-Tanner model is revisited to account for the influence of a transmissible disease, under the assumption that it spreads among the prey species only. We have found the equilibria and analyzed the behavior of the system around each one of them. A threshold result determining when the disease dies out has been identified. We also investigated the parametric space under which the system enters into Hopf and transcritical bifurcations, around the disease free equilibrium. The system is shown to experience neither saddle-node nor pitch-fork bifurcation. Global stability results are obtained by constructing suitable Lyapunov functions.     

The effect of predation on the prevalence and aggregation of pathogens in prey

Although pathogens and predators have been widely used as bio-control agents against problematic prey species, little has been done to examine the prevalence and aggregation of pathogens in spatially structured eco-epidemiological systems. Here, we present a spatial model of a predator-prey/host-parasite system based on pair approximation and spatially stochastic simulations, with the predation pressure indicated by predator abundance and predation rates. Susceptible prey can not only be infected by contacting adjacent infected individuals but also by the global transmission of pathogens. The disease prevalence was found to follow a hump-shaped function in response to predation pressure. Moreover, predation pressure was not always negatively correlated with pathogen aggregation as proposed from empirical studies, but depending on the level of predation pressure. Highly connected site network facilitated the parasites infection, especially under high predation pressure. However, the connectivity of site network had no effect on the prevalence and aggregation of pathogens that can infect health prey through global transmission. It is thus possible to better design biological control strategies for target species by manipulating predation pressure and the range of pathogen transmission.     

一类食饵种群中具有传染病的捕食-被捕食系统

对疾病仅在食饵种群传播的有比例依赖的捕食-被捕食系统的动力学进行了分析,给出了每个平衡点附近系统的性态,定义了决定疾病灭绝和成为地方病的阁值R_0．得出的结论是:在比例依赖的捕食-被捕食系统中,染病食饵种群可以充当一个生物控制量,以抑制种群的绝灭．