A double age-structured model of the co-infection of tuberculosis and HIV

Kapitanov, G

doi:10.3934/mbe.2015.12.23

Cited by 10 publications

(5 citation statements)

References 11 publications

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“…(Naresh et al [72] is notable and unusual for considering the population-level impact of TB on HIV, however.) Kapitanov [74] introduces and analyses a PDE model, separately including time-since-infection for HIV and M. tuberculosis.…”

Section: Population-level Impact Of Hiv On Tb Epidemicsmentioning

confidence: 99%

Modelling the HIV-Associated TB Epidemic and the Impact of Interventions Aimed at Epidemic Control

Dodd

Pretorius

Williams

2019

HIV and Tuberculosis

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In this chapter, we focus on mathematical models of tuberculosis epidemiology (TB) that include interactions with HIV and an explicit representation of transmission. We review the natural history of TB and illustrate how its features are simplified and incorporated in mathematical models. We then review the ways HIV influences the natural history of TB, the interventions that have been considered in models, and the way these individual-level effects are represented in models. We then go on to consider population-level effects, reviewing the TB/HIV modelling literature. We first review studies whose focus was on purely epidemiological modelling, and then studies whose focus was on modelling the impact of interventions. We conclude with a summary of the uses and achievements of TB/HIV modelling and some suggested future directions.

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Section: Population-level Impact Of Hiv On Tb Epidemicsmentioning

confidence: 99%

Modelling the HIV-Associated TB Epidemic and the Impact of Interventions Aimed at Epidemic Control

Dodd

Pretorius

Williams

2019

HIV and Tuberculosis

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“…A variety of epidemiological models allow for one or the other type of structure [27][28][29][30], starting with a seminal article from the 1920s [23]. However, models allowing for a double continuous structure are rare [30][31][32][33][34][35][36][37], even though it is particularly suited to investigate infections such as COVID-19, with strong effects of host and infection age. Indeed, in addition to taking into account the age structure of the host population, as well as the gradient of disease severity from mild to critical symptoms, the model readily captures the variation in infectiousness as a function of the time since infection.…”

Section: Introductionmentioning

confidence: 99%

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

et al. 2021

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In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing.

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“…[16,31,50,54,58] and the references therein for a survey of such models. However, epidemiological models including both infection and chronological age are not so common in the literature (see [5,14,25,27,29,32,34,47,62] for an exhaustive list). In a context of vector-borne infectious diseases, and more precisely focusing on malaria transmission, models with both chronological and infection age structures have never been considered until now.…”

Section: Introductionmentioning

confidence: 99%

Human-vector malaria transmission model structured by age, time since infection and waning immunity

Richard¹,

Choisy²,

Lefèvre³

et al. 2020

Preprint

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In contrast to the many theoretical studies on the transmission of human-mosquitoes malaria infection, few studies have considered a multiple structure model formulations including (i) the chronological age of humans and mosquitoes population, (ii) the time since humans and mosquitoes are infected and (iii) humans waning immunity (i.e., the progressive loss of protective antibodies after recovery). Such structural variables are well documented to be fundamental for the transmission of human-mosquitoes malaria infections. Here we formulate an age-structured model accounting for the three structural variables. Using integrated semigroups theory, we first handle the well-posedness of the model proposed. We also investigate the existence of model's steady-states. A disease-free equilibrium always exists while the existence of endemic equilibria is discussed. We derive the threshold R 0 (the basic reproduction number). The expression of the R 0 obtained here particularly highlight the effect of above structural variables on key important epidemiological traits of the human-vector association. This includes, humans and mosquitoes transmission probability and survival rates. Next, we derive a necessary and sufficient condition that implies the bifurcation of an endemic equilibrium. In some configuration where the age-structure of the human population is neglected, we show that, depending on the sign of some constant C bif given by the parameters, a bifurcation occurs at R 0 = 1 that is either forward or backward. In the former case, it means that there exists a (unique) endemic equilibrium if and only if R 0 > 1. In the latter case, no endemic equilibrium exists for R 0 1 small enough, a unique exists if R 0 > 1 while multiple endemic equilibria exist when 0 R 0 < 1 close enough to 1.

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A double age-structured model of the co-infection of tuberculosis and HIV

Cited by 10 publications

References 11 publications

Modelling the HIV-Associated TB Epidemic and the Impact of Interventions Aimed at Epidemic Control

Modelling the HIV-Associated TB Epidemic and the Impact of Interventions Aimed at Epidemic Control

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

Human-vector malaria transmission model structured by age, time since infection and waning immunity

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