  Malaria is a vector-borne disease that exacts a grave toll in the Global
South. The epidemiology of Plasmodium vivax, the most geographically expansive
agent of human malaria, is characterised by the accrual of a reservoir of
dormant parasites known as hypnozoites. Relapses, arising from hypnozoite
activation events, comprise the majority of the blood-stage infection burden,
with implications for the acquisition of immunity and the distribution of
superinfection. Here, we construct a hybrid transmission model for P. vivax
that concurrently accounts for the accrual of the hypnozoite reservoir,
(blood-stage) superinfection and the acquisition of immunity. We begin by
analytically characterising within-host dynamics as a function of
mosquito-to-human transmission intensity, extending our previous model
(comprising an open network of infinite server queues) to capture a discretised
immunity level. To model transmission-blocking and antidisease immunity, we
allow for geometric decay in the respective probabilities of successful
human-to-mosquito transmission and symptomatic blood-stage infection as a
function of this immunity level. Under a hybrid approximation -- whereby
probabilistic within-host distributions are cast as expected population-level
proportions -- we couple host and vector dynamics to recover a deterministic
compartmental model in line with Ross-Macdonald theory. We then perform a
steady-state analysis for this compartmental model, informed by the (analytic)
distributions derived at the within-host level. To characterise transient
dynamics, we derive a reduced system of integrodifferential equations (IDEs),
likewise informed by our within-host queueing network, allowing us to recover
population-level distributions for various quantities of epidemiological
interest. Our model provides insights into important, but poorly understood,
epidemiological features of P. vivax.
