ABSTRACT
However, the dynamics of z:; depend on the infected host population, I,. The following theorem gives sufficient conditions for persistence or extinction of the infection in the host population. The results depend on the value of the threshold Ro, where Ro is defined by
Ro = AK = u(E•:;:J At;U;w•;(2-cS,;))K
b b , {8)
where A = u[EiSJ >.iJPsP;WsJ (2 - cSi; )]. Before we state and prove the theorem, some additional facts are needed. Let zM denote the value where the function h defined by
h(z) = z(1 -b) + (K-z)(1 - e-A•) (9) assumes its maximum on (0, K); zM is unique. In addition, let x denote the unique positive fixed point of h when Ro > 1. The values of x and zM are very important in the next Theorem and Lemma.
