lecture+14+Infectious+Disease

# A d vi where a is the death rate due to the disease v

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a + d + v)I where a is the death rate due to the disease v is the rate of recovery to immunity Recovered (and Immune) dR/dt = vI dR

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Equilibrium for Disease to Spread We model cases of the disease, not the population size of the individual disease organisms. The equation for infected individuals is the key one in this system: where dI/dt is positive, the disease will spread in a population. We can solve for the equilibrium point for I, yielding: b *S*I=( a + d + v)*I b *S = ( a + d + v) and we can define 1/( a + d + v) as the longevity of the disease L. Spread of the disease will then be proportional to b *S*L; the disease will spread (dI/dt > 0) if b *S*L > 1
Dynamics of disease-host interaction The disease/host system is modeled in a way very similar to the predator/prey system Like the predator/prey system, the disease/host system can give rise to oscillations and in practice oscillations have been observed frequently

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Measles before the vaccines occurred cyclically
Threshold Host Population There should also be a threshold population for diseases; when a disease is just entering a population, S represents almost all of N (the overall population), and we can rearrange: b *S*L = 1 to yield N T = 1/(b*L)

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