An immigration-death model to estimate the duration of malaria infection when detectability of the parasite is imperfect.

Immigration-death models are proposed to analyse the infection dynamics in longitudinal studies of panels of heavily parasitized human hosts where parasites have been typed at regular intervals by PCR. Immigration refers to the acquisition of a new parasitic genotype, occurring at rate lambda, and death refers to the clearance of a parasitic genotype (with rate mu). The models assume that corresponding to each observed process which is the detection or failure to detect a parasitic genotype, is an underlying true process which is hidden as a result of imperfect detection. We consider: (i) a model in which no distinction is made between the different members of the human population, who collectively represent the habitat of the parasites, and (ii) a model that allows for the accrual of infections with age. The models are fitted to a panel data set of malaria genotype of parasites belonging to the msp2 FC27 and 3D7 allelic families from a study of the dynamics of Plasmodium falciparum in Northern Ghana. Maximum likelihood estimates suggest that on average any individual residing in this holo-endemic area will acquire 16 new infections per year (95 per cent CI, 15-18) (defined by their single locus genotypes) and that infection with any of these genotypes lasts on average 152 days (95 per cent CI, 138-169). We estimate that an average of 47 per cent (95 per cent CI, 42-51) of the parasite types present in the host are detected in a finger-prick blood sample. This model provides a basis for analyses of how these quantities vary with the age, and hence the immune status of the host.