Management -AW-Q 97

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1. In class we derived a susceptible-infected model of host-pathogen interactions. We focused primarily on the dynamics of the infected class, lumping the loss of infecteds due to recovery and death into a single parameter (m). For this question, you will build upon the model we developed in class.

(a) Write the full expressions for the dynamics of susceptible and infected hosts, assuming that some infected hosts die from infection while others recover, becoming susceptible again. Note that you will now need to represent death and recovery processes independently. Please use the symbols ‘c’ for the per-capita recovery rate and ‘d’ for the per-capita death rate of infected hosts due to infection. Label each term in your equations, using arrows or brackets, with the biological interpretation of the term (e.g., “loss of susceptibles to infection” and “gain of new infections”). (8 points)

(b) Using your response to part (a), derive the threshold density of susceptible hosts that is required for the pathogen to spread through the host population. (4 points)

(c) Imagine that you designing a management plan to prevent disease outbreaks in a herd of elk, and that you are limited to one of these three options
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1. Increase the recovery rate so that infected animals clear the pathogen more quickly.
2. Decrease the death rate so that infect animals survive longer, but they do not clear the

3. Both: Increase recovery rate AND decrease the death rate.Which of these options would be most likely to limit the spread of a disease in the elk herd?Your answer should be based on your response to part (b), and please explain your logic in words. (4 points)
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