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Let $p(a)$ be the true seroprevalence at age $a$, and $\lambda (a)$ the force of infection, meaning the instantaneous rate of a first infection among people still uninfected. In an irreversible serocatalytic model, people begin seronegative and retain detectable antibodies after infection. Their seronegative fraction $s(a)=1-p(a)$ obeysHenceEquivalently, where differentiation is possible, $\lambda (a)=p^{\prime }(a)/[1-p(a)]$. This identifies the force of infection as a hazard function and $1-p(a)$ as the survival function for remaining uninfected. For constant exposure $\lambda$, $p(a)=1-e^{-\lambda a}$. A single calendar-time survey reflects each birth cohort's accumulated exposure; interpreting the same age curve as a timeless age effect requires assumptions about historical transmission.

A susceptible person must have the same annual force of infection at every age. Thus the difference between age groups is their length of exposure, not an age-dependent infection hazard. To interpret one fitted constant as a historical annual force of infection, also assume that this common rate was sufficiently stable over the calendar years represented by the sampled birth cohorts. Otherwise an age pattern can reflect past outbreaks or cohort exposure, and the fitted constant is only a model-dependent summary. Representative sampling and comparable antibody detection across ages are additional conditions on interpreting the observed seroprevalence.

Before introduction there is no local infection exposure. Let $H=2024-2005=19$ years, using the actual elapsed time between introduction and sampling if exact dates are available. A lifelong resident aged $a_i$ has therefore had onlyyears of possible exposure. With a constant post-introduction force of infection $\lambda$, replace age by this exposure duration:Fit the same binomial regression with $\ln e_i$ as its offset. The predicted seroprevalence increases with age up to 19 and then reaches a plateau, since older residents all began local exposure at introduction.

This is equivalent to using a calendar-time force of infection of zero before 2005 and $\lambda$ afterwards. With a changing post-introduction rate, the more general exposure is ${\int }_{\max (2005,2024-a_i)}^{2024}\lambda (u)du$. Account separately for migration or infection acquired elsewhere, since current residence alone need not specify lifetime exposure. Subjects with exactly zero exposure have model probability zero and cannot be included by taking $\ln 0$ as an ordinary finite offset; handle them through the original probability 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.

Seroprevalence is the proportion of a specified population with a positive result for a specified antibody assay. Its biological interpretation depends on assay diagnostic sensitivity, diagnostic specificity and the persistence and origin of the measured antibodies. It is not itself the incidence rate of new infection.