An age-structured epidemic model for the demographic transition

Inaba, Hisashi; Saito, Ryohei; Bacaër, Nicolas

doi:10.1007/s00285-018-1253-7

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…Quoique encore incomplète d'un point de vue mathématique, notre étude est néanmoins plus précise que celle du modèle analogue de [19]. On a vu que même pour un système d'équations différentielles ordinaires homogènes, l'étude de la stabilité linéaire n'est pas triviale, tandis que la stabilité globale nous échappe encore.…”

Section: Discussionunclassified

Ein mathematisches Modell für einen partiellen demographischen Übergang

Bacaër

Inaba²,

Moussaoui

2021

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

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Wir schlagen ein System gewöhnlicher Differentialgleichungen mit homogenen nichtlinearen Termen des ersten Grades vor, um den demografischen Übergang zu modellieren. Es gibt zwei Altersgruppen und zwei Fruchtbarkeitsstufen. Eine geringe Fruchtbarkeit erstreckt sich durch Mimikry auf Erwachsene mit hoher Fruchtbarkeit. Wenn der Mimikry-Koeffizient zunimmt, überschreitet die Bevölkerung zwei Schwellenwerte. Zwischen diesen beiden Schwellenwerten nimmt die Population mit einer stabilen Mischung der beiden Fertilitätsraten exponentiell zu oder ab. Dieser teilweise demografische Übergang ist in einigen Ländern Afrikas südlich der Sahara zu beobachten. We study a mathematical model for the demographic transition. It is a homogeneous differential system of degree one. There are two age groups and two fertility levels. Low fertility extends by mimicry to adults with high fertility. When the mimicry coefficient increases, the system crosses two thresholds between which the population increases or decreases exponentially with a stable mixture of the two fertility rates. This partial demographic transition is reminiscent of the situation in some countries of sub-Saharan Africa. On propose un système d'équations différentielles ordinaires avec des termes non linéaires homogènes de degré un pour modéliser la transition démographique. Il y a deux classes d'âge et deux niveaux de fécondité. La fécondité faible s'étend par mimétisme aux adultes avec une fécondité élevée. Lorsque le coefficient de mimétisme augmente, la population traverse deux seuils. Entre ces deux seuils, la population croît ou décroît exponentiellement avec un mélange stable des deux fécondités. Cette transition démographique partielle s'observe dans certains pays d'Afrique subsaharienne.

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Section: Discussionunclassified

Ein mathematisches Modell für einen partiellen demographischen Übergang

Bacaër

Inaba²,

Moussaoui

2021

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

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“…However, this does not consider one patient, but rather takes a population-representative approach. There are model calculations that were, for example, already made in the early 1980s [19], and which show that there are demographic transitions that must be considered in the course of population development [20,21].…”

Section: Transition Models In Generalmentioning

confidence: 99%

On the Necessity of a Geriatric Oral Health Care Transition Model: Towards an Inclusive and Resource-Oriented Transition Process

Nitschke

Haffner

et al. 2022

IJERPH

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People in need of care also require support within the framework of structured dental care in their different life situations. Nowadays, deteriorations in oral health tend to be noticed by chance, usually when complaints or pain are present. Information on dental care is also lost when life situations change. An older person may rely on family members having oral health skills. This competence is often not available, and a lot of oral health is lost. When someone, e.g., a dentist, physician, caregiver, or family member notices a dental care gap, a structured transition to ensure oral health should be established. The dental gap can be detected by, e.g., the occurrence of bad breath in a conversation with the relatives, as well as in the absence of previously regular sessions with the dental hygienist. The aim of the article is to present a model for a structured geriatric oral health care transition. Due to non-existing literature on this topic, a literature review was not possible. Therefore, a geriatric oral health care transition model (GOHCT) on the basis of the experiences and opinions of an expert panel was developed. The GOHCT model on the one hand creates the political, economic, and legal conditions for a transition process as a basis in a population-relevant approach within the framework of a transition arena with the representatives of various organizations. On the other hand, the tasks in the patient-centered approach of the transition stakeholders, e.g., patient, dentist, caregivers and relatives, and the transition manager in the transition process and the subsequent quality assurance are shown.

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“…Kuniya [16] studied the global asymptotic stability by discretizing the age-structured multigroup model. Inaba et al [17] established an age-structured model of epidemic spreading for the demographic transition and obtained the stability condition using reproduction numbers. So et al [18] derived the equation of a reaction-diffusion model for a single species population with the age structure.…”

Section: Introductionmentioning

confidence: 99%

Epidemic Spreading Combined with Age and Region in Complex Networks

Zhang

Song

Wang

et al. 2020

Mathematical Problems in Engineering

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In social networks, the age and the region of individuals are the two most important factors in modeling infectious diseases. In this paper, a spatial susceptible-infected-susceptible (SIS) model is proposed to describe epidemic spreading over a network with region and age by establishing several partial differential equations. Numerical simulations are performed, and the simulation of the proposed model agrees well with real influenza-like illness (ILI) in the USA reported by the Centers for Disease Control (CDC). Moreover, the proposed model can be used to predict the infected density of individuals. The results show that our model can be used as a tool to analyze influenza cases in the real world.

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An age-structured epidemic model for the demographic transition

Cited by 6 publications

References 17 publications

Ein mathematisches Modell für einen partiellen demographischen Übergang

Ein mathematisches Modell für einen partiellen demographischen Übergang

On the Necessity of a Geriatric Oral Health Care Transition Model: Towards an Inclusive and Resource-Oriented Transition Process

Epidemic Spreading Combined with Age and Region in Complex Networks

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