Serocatalytic model
= Serocatalytic model
An irreversible <serocatalytic model> describes the transition from seronegative to seropositive after infection. If the <force of infection> is $\lambda(a)$ and detectable <antibodies> persist, the seronegative fraction satisfies $s'(a)=-\lambda(a)s(a)$, hence <seroprevalence> is $1-\exp[-\int_0^a\lambda(u)\,du]$ when $s(0)=1$. Antibody loss needs a reverse transition, and imperfect testing needs a separate observation model.