A hybrid model for the effects of treatment and demography on malaria superinfection

A hybrid transmission model for Plasmodium vivax accounting for superinfection, immunity and the hypnozoite reservoir

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 novel model for the transmission of P. vivax that concurrently accounts for the accrual of the hypnozoite reservoir, (blood-stage) superinfection and the acquisition of immunity. We begin by using an infinite-server queueing network model to characterise the within-host dynamics as a function of mosquito-to-human transmission intensity, extending our previous model 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, likewise informed by our within-host queueing network, allowing us to recover population-level distributions for various quantities of epidemiological interest. In capturing the interplay between hypnozoite accrual, superinfection and acquired immunity-and providing, to the best of our knowledge, the most complete population-level distributions for a range of epidemiological values-our model provides insights into important, but poorly understood, epidemiological features of P. vivax.

Quantifying the impact of interventions against Plasmodium vivax: A model for country-specific use

In order to evaluate the impact of various intervention strategies on Plasmodium vivax dynamics in low endemicity settings without significant seasonal pattern, we introduce a simple mathematical model that can be easily adapted to reported case numbers similar to that collected by surveillance systems in various countries. The model includes case management, vector control, mass drug administration and reactive case detection interventions and is implemented in both deterministic and stochastic frameworks. It is available as an R package to enable users to calibrate and simulate it with their own data. Although we only illustrate its use on fictitious data, by simulating and comparing the impact of various intervention combinations on malaria risk and burden, this model could be a useful tool for strategic planning, implementation and resource mobilization.

Superinfection and the hypnozoite reservoir for Plasmodium vivax: a general framework

A characteristic of malaria in all its forms is the potential for superinfection (that is, multiple concurrent blood-stage infections). An additional characteristic of Plasmodium vivax malaria is a reservoir of latent parasites (hypnozoites) within the host liver, which activate to cause (blood-stage) relapses. Here, we present a model of hypnozoite accrual and superinfection for P. vivax. To couple host and vector dynamics for a homogeneously-mixing population, we construct a density-dependent Markov population process with countably many types, for which disease extinction is shown to occur almost surely. We also establish a functional law of large numbers, taking the form of an infinite-dimensional system of ordinary differential equations that can also be recovered by coupling expected host and vector dynamics (i.e. a hybrid approximation) or through a standard compartment modelling approach. Recognising that the subset of these equations that model the infection status of the human hosts has precisely the same form as the Kolmogorov forward equations for a Markovian network of infinite server queues with an inhomogeneous batch arrival process, we use physical insight into the evolution of the latter process to write down a time-dependent multivariate generating function for the solution. We use this characterisation to collapse the infinite-compartment model into a single integrodifferential equation (IDE) governing the intensity of mosquito-to-human transmission. Through a steady state analysis, we recover a threshold phenomenon for this IDE in terms of a parameter [Formula: see text] expressible in terms of the primitives of the model, with the disease-free equilibrium shown to be uniformly asymptotically stable if [Formula: see text] and an endemic equilibrium solution emerging if [Formula: see text]. Our work provides a theoretical basis to explore the epidemiology of P. vivax, and introduces a strategy for constructing tractable population-level models of malarial superinfection that can be generalised to allow for greater biological realism in a number of directions.

Measuring changes in Plasmodium falciparum census population size in response to sequential malaria control interventions

Here we introduce a new endpoint "census population size" to evaluate the epidemiology and control of Plasmodium falciparum infections, where the parasite, rather than the infected human host, is the unit of measurement. To calculate census population size, we rely on a definition of parasite variation known as multiplicity of infection (M O I v a r ), based on the hyper-diversity of the v a r multigene family. We present a Bayesian approach to estimate M O I v a r from sequencing and counting the number of unique DBLα tags (or DBLα types) of v a r genes, and derive from it census population size by summation of M O I v a r in the human population. We track changes in this parasite population size and structure through sequential malaria interventions by indoor residual spraying (IRS) and seasonal malaria chemoprevention (SMC) from 2012 to 2017 in an area of high-seasonal malaria transmission in northern Ghana. Following IRS, which reduced transmission intensity by > 90% and decreased parasite prevalence by ~40-50%, significant reductions in v a r diversity, M O I v a r , and population size were observed in ~2,000 humans across all ages. These changes, consistent with the loss of diverse parasite genomes, were short lived and 32-months after IRS was discontinued and SMC was introduced, v a r diversity and population size rebounded in all age groups except for the younger children (1-5 years) targeted by SMC. Despite major perturbations from IRS and SMC interventions, the parasite population remained very large and retained the v a r population genetic characteristics of a high-transmission system (high v a r diversity; low v a r repertoire similarity) demonstrating the resilience of P. falciparum to short-term interventions in high-burden countries of sub-Saharan Africa.