  Malaria is a mosquito-borne disease with a devastating global impact.
Plasmodium vivax is a major cause of human malaria beyond sub-Saharan Africa.
Relapsing infections, driven by a reservoir of liver-stage parasites known as
hypnozoites, present unique challenges for the control of P. vivax malaria.
Following indeterminate dormancy periods, hypnozoites may activate to trigger
relapses. Clearance of the hypnozoite reservoir through drug treatment (radical
cure) has been proposed as a potential tool for the elimination of P. vivax
malaria. Here, we introduce a stochastic, within-host model to jointly
characterise hypnozoite and infection dynamics for an individual in a general
transmission setting, allowing for radical cure. We begin by extending an
existing activation-clearance model for a single hypnozoite, adapted to both
short- and long-latency strains, to include drug treatment. We then embed this
activation-clearance model in an epidemiological framework accounting for
repeated mosquito inoculation and the administration of radical cure. By
constructing an open network of infinite server queues, we derive analytic
expressions for several quantities of epidemiological significance, including
the size of the hypnozoite reservoir; the relative contribution of relapses to
the infection burden; the distribution of multiple infections; the cumulative
number of recurrences over time, and the time to first recurrence following
drug treatment. By deriving, rather than assuming parameteric forms, we
characterise the transient dynamics of the hypnozoite reservoir following
radical cure more accurately than previous approaches. To yield
population-level insights, our analytic within-host distributions can be
embedded in multiscale models. Our work thus contributes to the epidemiological
understanding of the effects of radical cure on P. vivax malaria.
