Age Structures in Mathematical Models for Infectious Diseases, with a Case Study of Respiratory Syncytial Virus

Hogan, Alexandra B.; Glass, Kathryn M.; Moore, Hannah C; Anderssen, R. S.

doi:10.1007/978-4-431-55342-7_9

Cited by 7 publications

(10 citation statements)

References 36 publications

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“…From system (3), it can be seen that the hypothesis [H 1 ], is biologically correct, since these represent time lapses and contact rates. Moreover, the presumption for β 1 (t) and β 2 (t) in [H 2 ] is a natural way to introduce seasonality in these types of models (White et al 2005;Hogan et al 2016a;Arenas et al 2008). Now, from condition [H 3 ] , if there are no infectives, then there is no contact between susceptible and infectives, which is biologically natural for the this mathematical model (3).…”

Section: Notation and Preliminary Resultsmentioning

confidence: 99%

“…In particular, we study the existence and the analytical behavior of a S i , E i , I i , R i type model. This model is based on a deterministic ordinary differential equation system, where the force of infection is given by a function β i (t) f (I 1 (t), I 2 (t))), which generalizes the models presented in Hogan et al (2016b), White et al (2005), White et al (2007), Weber et al (2001), Hogan et al (2016a) and Hogan et al (2017). We employ some interesting ideas used in related works in mathematical modeling in epidemiology (Luca et al 2018;Capasso and Serio 1978;Guerrero-Flores et al 2019;Mateus and Silva 2017;Valle et al 2013; Blackwood and Childs 2018; Gölgeli and Atay 2020; Safi and Garba 2012; Jia and Zhang 2014).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

2021

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In this article, we study the dynamics of a new proposed age-structured population mathematical model driven by a seasonal forcing function that takes into account the variability of the climate. We introduce a generalized force of infection function to study different potential disease outcomes. Using nonlinear analysis tools and differential inequalities theorems, we obtain sufficient conditions that guarantee the existence of a positive periodic solution. Moreover, we provide sufficient conditions that assure the global attractivity of the positive periodic solution. Numerical results corroborate the theoretical results in the sense that the solutions are positive and the periodic solution is a global attractor. This type of models are important, since they take into account the variability of the weather and the impact on some epidemics such as the current COVID-19 pandemic.

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Section: Notation and Preliminary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

2021

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“…Given that we examined the broad population-level impacts in a large population, we considered this a reasonable model simplification. Furthermore, it has been shown that, for a similar compartmental RSV model, including multiple age classes did not change the bifurcation structure of the model [ 51 ]. However, different vaccine candidates for RSV are being developed for distinct key age groups: infants, young children, pregnant women and the elderly [ 28 ].…”

Section: Discussionmentioning

confidence: 99%

Unexpected Infection Spikes in a Model of Respiratory Syncytial Virus Vaccination

2017

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Respiratory Syncytial Virus (RSV) is an acute respiratory infection that infects millions of children and infants worldwide. Recent research has shown promise for the development of a vaccine, with a range of vaccine types now in clinical trials or preclinical development. We extend an existing mathematical model with seasonal transmission to include vaccination. We model vaccination both as a continuous process, applying the vaccine during pregnancy, and as a discrete one, using impulsive differential equations, applying pulse vaccination. We develop conditions for the stability of the disease-free equilibrium and show that this equilibrium can be destabilised under certain extreme conditions, even with 100% coverage using an (unrealistic) vaccine. Using impulsive differential equations and introducing a new quantity, the impulsive reproduction number, we showed that eradication could be acheived with 75% coverage, while 50% coverage resulted in low-level oscillations. A vaccine that targets RSV infection has the potential to significantly reduce the overall prevalence of the disease, but appropriate coverage is critical.

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“…Hasil simulasi dari metode Transformasi Diferensial Multi Step akan dibandingkan dengan metode Runge-kutta yang merupakan metode yang paling sering digunakan untuk menyelesaikan sistem persamaan diferensial. Nilai parameter yang digunakan adalah β = 0.5 day −1 , δ = 1/4 day −1 , µ = 1/(65 × 365) day −1 , v = 1/20, γ = 1/10 day −1[12].Gambar 1 menunjukkan bahwa TDM dan Metode Rungge-Kutta memberikan solusi yang serupa. Untuk model SEIRS autonomous, kedua metode memberikan solusi yang serupa dan time-step adalah 0.01.…”

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Konstruksi Metode Transformasi Diferensial Multi-Step (Multi-Step Differential Transform Method) untuk Model SEIRS Autonomous dan Nonautonomous

Bunga¹,

Pahnael²,

Lobo³

et al. 2020

jmi

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Pemodelan matematika telah banyak digunakan untuk memahami permasalahan nyata. Model matematika dapat diselesaikan secara analitik. Namun, apabila model matematika tersebut semakin kompleks, maka solusi analitik tidak mudah diperoleh dan pendekatan numerik digunakan. Dalam artikel ini, pendekatan numerik dengan Metode Transformasi Diferensial (MTD) \textit{multi-step} yang menghasilkan solusi deret konvergen digunakan untuk mencari solusi dari model matematika penyebaran penyakit SEIRS yang \textit{autonomous} dan \textit{non-autonomous}. Metode ini dikenal juga dengan metode semi analitik karena kita dapat menuliskan solusi analitik dari model yang dicarikan solusinya. Dalam artikel akan dikonstruksi metode tranformasi diferensial untuk model SEIRS \textit{autonomous} dan \textit{nonautonomous} dan menganalisis akurasi dengan cara membandingkan dengan metode Runge-Kutta. Metode transformasi diferensial \textit{multi-step} dapat memberikan aproksimasi solusi yang baik dari model matematika SEIRS \textit{autonomous} dan \textit{non-autonomous}. Namun, kinerja dari metode ini lebih baik pada model \textit{autonomous}.}}

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Age Structures in Mathematical Models for Infectious Diseases, with a Case Study of Respiratory Syncytial Virus

Cited by 7 publications

References 36 publications

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

Unexpected Infection Spikes in a Model of Respiratory Syncytial Virus Vaccination

Konstruksi Metode Transformasi Diferensial Multi-Step (Multi-Step Differential Transform Method) untuk Model SEIRS Autonomous dan Nonautonomous

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