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 $s^{\prime }(a)=-\lambda (a)s(a)$, 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.