Lecture_4_Microparasites2 - 1/20/2009 Equations Population...

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1/20/2009 1 Population biology of microparasites microparasites II: population II: population impacts and vaccination Equations S usceptible nfected Death Death b α +b β dS dt = a(S+I+R) - bS - β SI d a I R ecovered Death b γ dI dt = β SI- bI- α I - γ I dR dt = γ I - bR Basic reproductive number Parasite establishment will be most strongly influenced by R 0 ‐‐ The Basic Reproductive Number Equivalent to the parasite’s fitness or ‘birth rate’ early in an epidemic γ α β + + b S R o = Speed and magnitude of epidemic 4000 5000 6000 ed hosts R 0 =6 R 0 =3 0 1000 2000 3000 0 5 10 15 Time Number infect R 0 =1.5 Threshold density for pathogen establishment establishment (N (N T ) + + = d N T Highly virulent pathogens or those from which hosts recover fast may not establish without a large number of susceptible hosts Critical community size (CCS) Smallest population of susceptible hosts below which pathogen goes extinct, and above which pathogen persists Note: N T = invasion threshold CCS = persistence threshold
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1/20/2009 2 Vaccination Root “vacca” = Latin for cow Vaccination Goals Protect the individual from infection Individual immunity 8 Protect the population from an epidemic “Herd immunity”
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This note was uploaded on 09/22/2009 for the course ECOL 4150 taught by Professor Prin during the Spring '08 term at University of Georgia Athens.

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Lecture_4_Microparasites2 - 1/20/2009 Equations Population...

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