Periodic solutions of an age-structured epidemic model with periodic infection rate

Hao Kang; Shigui Ruan; Qimin Huang

doi:10.3934/cpaa.2020220

Periodic solutions of an age-structured epidemic model with periodic infection rate

Hao Kang, Shigui Ruan, Qimin Huang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider an age-structured epidemic model of the susceptible-exposed-infectious-recovered (SEIR) type. To characterize the seasonality of some infectious diseases such as measles, it is assumed that the infection rate is time periodic. After establishing the well-posedness of the initial-boundary value problem, we study existence of time periodic solutions of the model by using a fixed point theorem. Some numerical simulations are presented to illustrate the obtained results.

Original language	English (US)
Pages (from-to)	4955-4972
Number of pages	18
Journal	Communications on Pure and Applied Analysis
Volume	19
Issue number	10
DOIs	https://doi.org/10.3934/cpaa.2020220
State	Published - Oct 2020

Keywords

Age-structure
Basic reproduction number
Periodic solution
SEIR epidemic model
Vaccination

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Periodic solutions of an age-structured epidemic model with periodic infection rate",

abstract = "In this paper we consider an age-structured epidemic model of the susceptible-exposed-infectious-recovered (SEIR) type. To characterize the seasonality of some infectious diseases such as measles, it is assumed that the infection rate is time periodic. After establishing the well-posedness of the initial-boundary value problem, we study existence of time periodic solutions of the model by using a fixed point theorem. Some numerical simulations are presented to illustrate the obtained results.",

keywords = "Age-structure, Basic reproduction number, Periodic solution, SEIR epidemic model, Vaccination",

author = "Hao Kang and Shigui Ruan and Qimin Huang",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary: 35Q92, 35C15; Secondary: 92B05. Key words and phrases. Age-structure, SEIR epidemic model, periodic solution, vaccination, basic reproduction number. Research was partially supported by National Science Foundation (DMS-1853622). ∗ Corresponding author.",

year = "2020",

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AU - Ruan, Shigui

AU - Huang, Qimin

N1 - Funding Information: 2020 Mathematics Subject Classification. Primary: 35Q92, 35C15; Secondary: 92B05. Key words and phrases. Age-structure, SEIR epidemic model, periodic solution, vaccination, basic reproduction number. Research was partially supported by National Science Foundation (DMS-1853622). ∗ Corresponding author.

PY - 2020/10

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N2 - In this paper we consider an age-structured epidemic model of the susceptible-exposed-infectious-recovered (SEIR) type. To characterize the seasonality of some infectious diseases such as measles, it is assumed that the infection rate is time periodic. After establishing the well-posedness of the initial-boundary value problem, we study existence of time periodic solutions of the model by using a fixed point theorem. Some numerical simulations are presented to illustrate the obtained results.

AB - In this paper we consider an age-structured epidemic model of the susceptible-exposed-infectious-recovered (SEIR) type. To characterize the seasonality of some infectious diseases such as measles, it is assumed that the infection rate is time periodic. After establishing the well-posedness of the initial-boundary value problem, we study existence of time periodic solutions of the model by using a fixed point theorem. Some numerical simulations are presented to illustrate the obtained results.

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KW - Basic reproduction number

KW - Periodic solution

KW - SEIR epidemic model

KW - Vaccination

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