A zoonotic disease is a disease that can be passed from animals to humans. Zoonotic viruses may adapt to a human host eventually becoming endemic in humans, but before doing so punctuated outbreaks of the zoonotic virus may be observed. The Ebola virus disease (EVD) is an example of such a disease. The animal population in which the disease agent is able to reproduce in sufficient number to be able to transmit to a susceptible human host is called a reservoir. There is little work devoted to understanding stochastic population dynamics in the presence of a reservoir, specifically the phenomena of disease extinction and reintroduction. Here, we build a stochastic EVD model and explicitly consider the impacts of an animal reservoir on the disease persistence. Our modelling approach enables the analysis of invasion and fade-out dynamics, including the efficacy of possible intervention strategies. We investigate outbreak vulnerability and the probability of local extinction and quantify the effective basic reproduction number. We also consider the effects of dynamic population size. Our results provide an improved understanding of outbreak and extinction dynamics in zoonotic diseases, such as EVD.
We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-KramersBrillouin) approximation is used to construct the optimal path to extinction. In addition, a probabilistic argument is used to understand the pre-extinction dynamics and approximate the mean time to extinction. Analytical results agree well with numerical Monte Carlo simulations. A control method is implemented to decrease the mean time to extinction. Analytical results quantify the effectiveness of the control and agree well with numerical simulations.
Pests and disease have become an increasingly common issue as globalized trade brings non-native species into unfamiliar systems. Emerald ash borer (Agrilus planipennis), is an Asiatic species of boring beetle currently devastating the native population of ash (Fraxinus) trees in the northern forests of the United States, with 85 million trees having already succumbed across much of the Midwest. We have developed a reaction-diffusion partial differential equation model to predict the spread of emerald ash borer over a heterogeneous 2-D landscape, with the initial ash tree distribution given by data from the Forest Inventory and Analysis. As expected, the model predictions show that emerald ash borer consumes ash which causes the local ash population to decline, while emerald ash borer spreads outward to other areas. Once the local ash population begins to decline emerald ash borer also declines due to the loss of available habitat. Our model’s strength lies with its focus on the county scale and its linkage between emerald ash borer population growth and ash density. This enables one to make accurate predictions regarding emerald ash borer spread which allows one to consider various methods of control as well as to accurately study the economic effects of emerald ash borer spread.
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