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

Henry, John M.

doi:10.1016/j.jtbi.2020.110194

Cited by 6 publications

(25 citation statements)

References 19 publications

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“…In the absence of demography (that is, human births and deaths), we can re-interpret the within-host PMF as the expected proportion of humans with hypnozoites in state ; a blood-stage infection comprising j parasite broods and having an immunity level k . Equation ( 1 ) can therefore be viewed as governing the expected proportion of humans in each hypnozoite/infection/immunity state (Henry 2020 ). In Sect.…”

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

confidence: 99%

“…We now construct hybrid transmission models (Nåsell 2013 ; Henry 2020 ) to couple host and vector dynamics. To the best of our knowledge, these models are novel in structure, in that hypnozoite densities, the multiplicity of blood-stage infection and an immunity level are explicitly included in the state space.…”

Section: Hybrid Transmission Models: Coupling Expected Host and Vecto...mentioning

confidence: 99%

“…Using the work of Barbour and Luczak ( 2012 ), we then recovered a deterministic (infinite) compartmental model as a functional law of large numbers; that is, we showed that the sample paths of the Markov process converged to a deterministic sample path in the infinite population size limit, when the number of mosquitoes per human was held fixed. We noted there, however, that an identical deterministic compartmental model could be recovered under a “hybrid approximation”, whereby host and vector dynamics are coupled through expected values, as per the construction of Nåsell ( 2013 ); Henry ( 2020 ). This hybrid construction is the focus of Sect.…”

Section: Hybrid Transmission Models: Coupling Expected Host and Vecto...mentioning

confidence: 99%

“…2.4 and 2.5 respectively. Section 3 concerns the construction of a novel hybrid transmission model (Nåsell 2013 ; Henry 2020 ), predicated on the coupling of expected host and vector dynamics. To recover the expected dynamics of the vector population, we consider the Kolmogorov forward differential equations for an underlying birth-death process (Sect.…”

Section: Introductionmentioning

confidence: 99%

“…To recover the expected dynamics of the vector population, we consider the Kolmogorov forward differential equations for an underlying birth-death process (Sect. 3.1 ); while observing that the within-host probability mass function (PMF) can be regarded as the expected population-level frequency distribution of hypnozoite, superinfection and immunity states (Henry 2020 ). We then couple host and vector dynamics in an infinite compartment model (Sect.…”

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...mentioning

confidence: 99%

Section: Hybrid Transmission Models: Coupling Expected Host and Vecto...mentioning

confidence: 99%

Section: Hybrid Transmission Models: Coupling Expected Host and Vecto...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 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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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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Quantifying the impact of interventions against Plasmodium vivax: A model for country-specific use

Champagne,

Gerhards,

Lana

et al. 2024

Epidemics

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

Cited by 6 publications

References 19 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

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

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

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