1. Eradication and Control Let R be the effective reproductive rate of a microparasite: Criterion for eradication:

2. Immunization Programmes If we immunized a proportion, p, of the susceptible population, the effective reproductive rate is at most: Where R0 is the basic reproductive rate. Clearly, if the following is true, then the eradication criterion is achieved.

3. Eradication and Control

4. In Terms of A and L

7. Immunization and new equilibria We can modify the SIR cohort model for immunization programme. We can modify the SIR cohort model for immunization programme. If we assume that fraction p of new borns are successfully immunized for an infection, we would only have to change the initial values of X and Z. If we assume that fraction p of new borns are successfully immunized for an infection, we would only have to change the initial values of X and Z. X(0)=(1-p)N(0) and Z(0)=pN(0) X(0)=(1-p)N(0) and Z(0)=pN(0)

8. SIR with Immunization Programme

12. Age Specific Immunization

13. Average Age of Infection For the new average age of infection, we simply take the first moment of the new lambda*X(a). We obtain: Type IType II

14. Average Age of Infection

15. Programme Specific Criteria Before, we assumed immunization for the entire population. Before, we assumed immunization for the entire population. What is our prediction for the age specific immunization program? What is our prediction for the age specific immunization program? We can obtain that information by taking the limit of the infection force to 0. We can obtain that information by taking the limit of the infection force to 0.

16. Programme Specific Criteria