A mathematical model of seropositivity to malaria antigen, allowing seropositivity to be prolonged by exposure

Malaria transmission intensity is traditionally estimated from entomological studies as the entomological inoculation rate (EIR), but this is labour intensive and also raises sampling issues due to the large variation from house to house. Incidence of malaria in the control group of a trial or in a cohort study can be used but is difficult to interpret and to compare between different places and between age groups because of differences in levels of acquired immunity. The reversible catalytic model has been developed to estimate malaria transmission intensity using age-stratified serological data. However, the limitation of this model is that it does not allow for persons to have their seropositivity boosted by exposure while they are already seropositive. The aim of this paper is to develop superinfection mathematical models that allow for antibody response to be boosted by exposure.

The superinfection models were fitted to age-stratified serological data using maximum likelihood method.

The results showed that estimates of seroconversion rate were higher using the superinfection model than catalytic model. This difference was milder when the level of transmission was lower. This suggests that the catalytic model is underestimating the transmission intensity by up to 31%. The duration of seropositivity is shorter with superinfection model, but still seems too long.

The model is important because it can produce more realistic estimates of the duration of seropositivity. This is analogous to Dietz model, which allowed for superinfection and produced more realistic estimates of the duration of infection as compared to the original Ross-MacDonald malaria model, which also ignores superinfection.