%0 Journal Article
%T Modeling Gender-Structured Wildlife Diseases with Harvesting: Chronic Wasting Disease as an Example
%A Mo'tassem Al-Arydah
%A Robert J. Smith
%A Frithjof Lutscher
%J ISRN Biomathematics
%D 2012
%R 10.5402/2012/802450
%X Chronic wasting disease (CWD) is a prion infectious disease that affects members of the deer family in North America. Concerns about the economic consequences of the presence of CWD have led management agencies to seek effective strategies to control CWD distribution and prevalence. Current mathematical models are either based on complex simulations or overly simplified compartmental models. We develop a mathematical model that includes gender structure to describe CWD in a logistically growing population. The model includes harvesting as a management strategy for the disease. We determine the stability conditions of the disease-free equilibrium for the model and calculate the basic reproduction number. We find an optimum interval of harvesting: with too little harvesting, the disease persists, whereas too much harvesting results in extinction of the population. A sensitivity analysis shows that the disease threshold is more sensitive to female than male harvesting and that harvesting has the greatest effect on the basic reproduction number. However, while harvesting may be a way to control CWD, the range of admissible harvesting rates may be very narrow, depending on other parameters. 1. Introduction Many wild animals come into contact with humans via harvesting, for meat, for pelts, or for population control. Transmissible diseases in wild populations pose a threat to ecology, the environment, and humans. Harvesting may also be a way that such disease transmission can be controlled; however, accurate harvesting of only sick animals is usually impractical or impossible. For example, many diseases have an extended latency period during which the animal is asymptomatic; as a result, targeted harvesting is not feasible. When targeted harvesting is impossible, harvesting for the sake of disease control has to be tightly balanced to ensure population survival. Mathematical models are important tools to determine optimal harvesting rates. A mathematical model should be as simple as possible to allow for easy parameterization and robust results; on the other hand, models need to include all important mechanisms of disease transmission and population behaviour. For example, if the latent period is comparable in duration to the life cycle of the animal, then incorporating population dynamics into a model becomes critical. Also, vertical transmission can sustain many diseases; in such cases, infection is passed from mother to offspring. Consequently, gender structure of the herd may play a crucial role in the life cycle of the disease. Conversely, many animals
%U http://www.hindawi.com/journals/isrn.biomathematics/2012/802450/