A semi-hybrid model for malaria with limited superinfection

Modelling malaria with consistency necessitates the introduction of at least two families of interconnected processes. Even in a Markovian context the simplest fully stochastic model is intractable and is usually transformed into a hybrid model, by supposing that these two families are stochastically independent and linked only through two deterministic connections. A model closer to the fully stochastic model is presented here, where one of the two families is subordinated to the other and just a unique deterministic connection is required. For this model a threshold theorem can be proved but the threshold level is not the one obtained in a hybrid model. The difference disappears only when the human population size approaches infinity.

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

Background

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.

Method

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

Results

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.

Conclusion

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.