Antibody Dynamics for Plasmodium vivax Malaria: A Mathematical Model

Mehra, Somya; McCaw, James M.; Flegg, Mark B.; Taylor, Peter G.; Flegg, Jennifer A.

doi:10.1007/s11538-020-00837-5

Cited by 10 publications

(19 citation statements)

References 34 publications

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“…2 , as an extension of previous simulations presented in Mehra et al. ( 2021 , 2022 ). We assume that the individual is both immune- and infection-naive at time zero, and is subject to a constant FORI year -1 .…”

Section: Within-host Human Dynamics: Hypnozoite Accrual Superinfectio...supporting

confidence: 69%

“…E The antibody level, as per the model introduced in Mehra et al. ( 2021 ), whereby the clearance of each blood-stage infection is associated with a unit boost of immunity that then decays exponentially (deterministically) with rate 1/250 day -1 …”

Section: Within-host Human Dynamics: Hypnozoite Accrual Superinfectio...mentioning

confidence: 99%

“…( 2022 ), this immunity level is governed by a shot noise process, akin to a previous model of antibody dynamics we introduced in Mehra et al. ( 2021 ). Rather than solving for the state probabilities based on the Kolmogorov forward differential equations for the queueing network (Sect.…”

Section: Introductionmentioning

confidence: 99%

“…2.2 ), we make use of the fact that the hypnozoites experience independent trajectories to derive a time dependent probability generating function (PGF) as in our previous work (Mehra et al. 2021 , 2022 ) (Sect. 2.3 ).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Within-host Human Dynamics: Hypnozoite Accrual Superinfectio...supporting

confidence: 69%

Section: Within-host Human Dynamics: Hypnozoite Accrual Superinfectio...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…as traffic, queues or caches models [3,16,24,25,28,37]. Poisson shot noise processes are also exploited to model earthquake aftershocks [38] and epidemics [31]. Spatial versions of {S t } t>0 are proposed in [1] to model the interference in wireless communication networks, see also [2,15,34,36].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of Poisson shot noise processes, and applications

Torrisi¹,

Leonardi²

2021

Preprint

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Poisson shot noise processes are natural generalizations of compound Poisson processes that have been widely applied in insurance, neuroscience, seismology, computer science and epidemiology. In this paper we study sharp deviations, fluctuations and the stable probability approximation of Poisson shot noise processes. Our achievements extend, improve and complement existing results in the literature. We apply the theoretical results to Poisson cluster point processes, including generalized linear Hawkes processes, and risk processes with delayed claims. Many examples are discussed in detail.

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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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Antibody Dynamics for Plasmodium vivax Malaria: A Mathematical Model

Cited by 10 publications

References 34 publications

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

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

Asymptotic analysis of Poisson shot noise processes, and applications

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

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