Now consider a wildlife population that is exposed to an infectious disease, with densities of susceptible and infected individuals given by S and I respectively. Use the information below to write down a set of ordinary differential equations that describe this system. • Susceptible hosts can reproduce at rate b and all offspring are born susceptible, but the disease prevents infected hosts from reproducing. • All hosts die at natural mortality rate d and infected hosts suffer further mortality at rate α. • Infectionoccursthroughdirectcontactofsusceptibleandinfectedhosts,withtheforceofinfectiongiven by βI. • Infected hosts can recover from disease at rate γ, but they do not gain immunity and instead return to being susceptible.

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Chapter2: Second-order Linear Odes
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Now consider a wildlife population that is exposed to an infectious disease, with densities of susceptible and infected individuals given by S and I respectively. Use the information below to write down a set of ordinary differential equations that describe this system. • Susceptible hosts can reproduce at rate b and all offspring are born susceptible, but the disease prevents infected hosts from reproducing. • All hosts die at natural mortality rate d and infected hosts suffer further mortality at rate α. • Infectionoccursthroughdirectcontactofsusceptibleandinfectedhosts,withtheforceofinfectiongiven by βI. • Infected hosts can recover from disease at rate γ, but they do not gain immunity and instead return to being susceptible.
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