1. General Epidemic SIR Transmission Plus Host Birth, Death Purpose: What fraction of hosts must be vaccinated in order to eradicate disease?

2. Compartments & Virulence Susceptible, Infective, Recovered Hosts Background Mortality: All classes Virulence: Extra mortality, Infected hosts Reproduction: All classes; Hosts Born S

3. Parameters b Per-capitum Birth  Transmission Rate (Mass Action) d Non-Disease Mortality (All) D Infective Mortality (D – d): Virulence > 0  Recovery from Infection

4. Dynamics of General Epidemic

5. Assumptions When Rare, Pathogen Invades Host Pop. R 0 > 1 Invasion Criterion Equilibrium: Endemic Infection Vaccine Available: What level of vaccination (reduction in susceptibility) would prevent disease form advancing when rare?

6. Analysis

7. Disease Control via Immunization Reduce S 0  S crit = S 1 S crit : Defined by R 0 = 1 Immunize Susceptible Hosts Too Few Hosts for Disease to Advance

8. Disease Control via Immunization More Virulent Disease, Lower R 0

9. Disease Control via Immunization Fraction Still Susceptible Fraction Immunize to Control Disease

10. Disease Control via Immunization Vaccinate p V S 0 Hosts Herd Immunity Vaccine Efficiency: Correction term N-Person Prisoner’s Dilemma ?

11. Vaccination Control (Ricklefs & Miller, 2000)

12. DiseaseLocaleR0R0 pVpV SmallpoxDeveloping World 3 - 50.7 – 0.8 MeaslesEngland130.92 Whooping cough England170.94 RubellaEngland60.83 Chicken PoxUS9 - 100.9 DiphtheriaUS4 - 60.8 Scarlet feverUS5 - 70.8 MumpsUS4 - 70.8 PolioNetherlands60.83 MalariaNigeria800.99 MalariaNigeria160.94 May, 1983; Includes corrections for vaccine efficiencies