A Multiscale Mathematical Model of Plasmodium Vivax Transmission

Anwar, Md Nurul; Hickson, Roslyn I.; Mehra, Somya; McCaw, James M.; Flegg, Jennifer A.

doi:10.1007/s11538-022-01036-0

Cited by 9 publications

(53 citation statements)

References 48 publications

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“…A multiscale mathematical model that accounts for hypnozoite variation within individuals without treatment has already been developed (Anwar 2022 ). In our previous work, we did not account for superinfection in the population level model.…”

Section: Methodsmentioning

confidence: 99%

“…Recovery without accounting for superinfection is straightforward. In our previous model (Anwar 2022 ), we did not account for superinfection in the population-level model while the within-host framework permits superinfection. Here, we consider superinfection at the population level by following the work of Mehra ( 2022 ).…”

Section: Methodsmentioning

confidence: 99%

“…Without treatment, blood-stage infections are cleared one at a time, but with treatment, blood-stage infections will all be cleared with probability . We define p ( t ) as the probability of blood-stage infected individuals having no hypnozoites in their liver (Anwar 2022 ). Therefore, at the time when radical cure is administered, individuals that were blood-stage infected either become susceptible with probability p ( t ) or become liver-stage infected with probability .…”

Section: Methodsmentioning

confidence: 99%

“…( 2022b ) have developed a within-host model capturing hypnozoite dynamics and variation across infected mosquito bites that explicitly models the effect of radical cure treatment on the hypnozoite dynamics and reservoir. We have previously developed a multiscale model (Anwar 2022 ) by embedding Mehra et al’s within-host model without treatment, which only uses three compartments at the population level while considering hypnozoite dynamics and the effect of the hypnozoite reservoir on disease transmission. The effect of three rounds of MDA with radical cure on P. vivax prevalence has been studied in a randomised controlled trial (Phommasone 2020 ).…”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 2 , we extend our existing multiscale model (Anwar 2022 ) to incorporate the effect of radical cure treatment and seasonality. We then obtain some key parameters for the population model from the within-host model (Mehra et al.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration

et al. 2023

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Plasmodium vivax is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driving this widespread phenomenon is the ability of the parasites to remain dormant in the liver. Known as ‘hypnozoites’, they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as ‘relapses’. As around 79–96% of infections are attributed to relapses from activating hypnozoites, we expect it will be highly impactful to apply treatment to target the hypnozoite reservoir (i.e. the collection of dormant parasites) to eliminate P. vivax. Treatment with radical cure, for example tafenoquine or primaquine, to target the hypnozoite reservoir is a potential tool to control and/or eliminate P. vivax. We have developed a deterministic multiscale mathematical model as a system of integro-differential equations that captures the complex dynamics of P. vivax hypnozoites and the effect of hypnozoite relapse on disease transmission. Here, we use our multiscale model to study the anticipated effect of radical cure treatment administered via a mass drug administration (MDA) program. We implement multiple rounds of MDA with a fixed interval between rounds, starting from different steady-state disease prevalences. We then construct an optimisation model with three different objective functions motivated on a public health basis to obtain the optimal MDA interval. We also incorporate mosquito seasonality in our model to study its effect on the optimal treatment regime. We find that the effect of MDA interventions is temporary and depends on the pre-intervention disease prevalence (and choice of model parameters) as well as the number of MDA rounds under consideration. The optimal interval between MDA rounds also depends on the objective (combinations of expected intervention outcomes). We find radical cure alone may not be enough to lead to P. vivax elimination under our mathematical model (and choice of model parameters) since the prevalence of infection eventually returns to pre-MDA levels.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration

et al. 2023

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

Mehra,

McCaw,

Taylor

2023

J. Math. Biol.

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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 $$R_0$$ R 0 expressible in terms of the primitives of the model, with the disease-free equilibrium shown to be uniformly asymptotically stable if $$R_0<1$$ R 0 < 1 and an endemic equilibrium solution emerging if $$R_0>1$$ R 0 > 1 . 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.

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

Mehra,

Taylor,

McCaw

et al. 2024

J. Math. Biol.

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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.

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A Multiscale Mathematical Model of Plasmodium Vivax Transmission

Cited by 9 publications

References 48 publications

Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration

Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration

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

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

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