Dynamical behavior of a rotavirus transmission model with an environmental effects

Isnani Darti; Agus Suryanto; Noraniza Bahrotul Ilmi

doi:10.1063/5.0023487

Dynamical behavior of a rotavirus transmission model with an environmental effects

Isnani Darti^*
, Agus Suryanto
, Noraniza Bahrotul Ilmi

^*Corresponding author for this work

Faculty of Mathematics and Natural Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

Rotavirus is one of the leading to severe diarrhea in infants and children throughout both developed and developing countries. Rotavirus infection is still a significant cause of death in infants and children. It has various mode of transmissions, those are, human to human, human to environment, and environment to human. In this paper, a SIRE (Susceptible, Infected, Recovered and Environment of pathogens) epidemic model is proposed and the dynamics of this model is analyzed by both theoretical and numerical means. Firstly, the basic reproduction number (R₀ ) which determines whether the disease is extinct or not, is derived. By Routh-Hurwitz criterion theory, we prove that the disease-free equilibrium is unstable and the endemic equilibrium is asymptotically stable when R₀ is greater than one. The analysis results are confirmed by some numerical simulations.

Original language	English
Title of host publication	Symposium on Biomathematics 2019, SYMOMATH 2019
Editors	Mochamad Apri, Vitalii Akimenko
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735420243
DOIs	https://doi.org/10.1063/5.0023487
Publication status	Published - 22 Sept 2020
Event	Symposium on Biomathematics 2019, SYMOMATH 2019 - Bali, Indonesia Duration: 25 Aug 2019 → 28 Aug 2019

Publication series

Name	AIP Conference Proceedings
Volume	2264
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	Symposium on Biomathematics 2019, SYMOMATH 2019
Country/Territory	Indonesia
City	Bali
Period	25/08/19 → 28/08/19

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Basic reproduction number
Next generation matrix
Rotavirus
Stability analysis

Access to Document

10.1063/5.0023487

Cite this

@inproceedings{aac52a3c390140258a23d90e2463ef37,

title = "Dynamical behavior of a rotavirus transmission model with an environmental effects",

abstract = "Rotavirus is one of the leading to severe diarrhea in infants and children throughout both developed and developing countries. Rotavirus infection is still a significant cause of death in infants and children. It has various mode of transmissions, those are, human to human, human to environment, and environment to human. In this paper, a SIRE (Susceptible, Infected, Recovered and Environment of pathogens) epidemic model is proposed and the dynamics of this model is analyzed by both theoretical and numerical means. Firstly, the basic reproduction number (R0 ) which determines whether the disease is extinct or not, is derived. By Routh-Hurwitz criterion theory, we prove that the disease-free equilibrium is unstable and the endemic equilibrium is asymptotically stable when R0 is greater than one. The analysis results are confirmed by some numerical simulations.",

keywords = "Basic reproduction number, Next generation matrix, Rotavirus, Stability analysis",

author = "Isnani Darti and Agus Suryanto and Ilmi, \{Noraniza Bahrotul\}",

note = "Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved.; Symposium on Biomathematics 2019, SYMOMATH 2019 ; Conference date: 25-08-2019 Through 28-08-2019",

year = "2020",

month = sep,

day = "22",

doi = "10.1063/5.0023487",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Mochamad Apri and Vitalii Akimenko",

booktitle = "Symposium on Biomathematics 2019, SYMOMATH 2019",

}

Darti, I , Suryanto, A & Ilmi, NB 2020, Dynamical behavior of a rotavirus transmission model with an environmental effects. in M Apri & V Akimenko (eds), Symposium on Biomathematics 2019, SYMOMATH 2019., 020001, AIP Conference Proceedings, vol. 2264, American Institute of Physics Inc., Symposium on Biomathematics 2019, SYMOMATH 2019, Bali, Indonesia, 25/08/19. https://doi.org/10.1063/5.0023487

Dynamical behavior of a rotavirus transmission model with an environmental effects. / Darti, Isnani ; Suryanto, Agus; Ilmi, Noraniza Bahrotul.
Symposium on Biomathematics 2019, SYMOMATH 2019. ed. / Mochamad Apri; Vitalii Akimenko. American Institute of Physics Inc., 2020. 020001 (AIP Conference Proceedings; Vol. 2264).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Dynamical behavior of a rotavirus transmission model with an environmental effects

AU - Darti, Isnani

AU - Suryanto, Agus

AU - Ilmi, Noraniza Bahrotul

PY - 2020/9/22

Y1 - 2020/9/22

N2 - Rotavirus is one of the leading to severe diarrhea in infants and children throughout both developed and developing countries. Rotavirus infection is still a significant cause of death in infants and children. It has various mode of transmissions, those are, human to human, human to environment, and environment to human. In this paper, a SIRE (Susceptible, Infected, Recovered and Environment of pathogens) epidemic model is proposed and the dynamics of this model is analyzed by both theoretical and numerical means. Firstly, the basic reproduction number (R0 ) which determines whether the disease is extinct or not, is derived. By Routh-Hurwitz criterion theory, we prove that the disease-free equilibrium is unstable and the endemic equilibrium is asymptotically stable when R0 is greater than one. The analysis results are confirmed by some numerical simulations.

AB - Rotavirus is one of the leading to severe diarrhea in infants and children throughout both developed and developing countries. Rotavirus infection is still a significant cause of death in infants and children. It has various mode of transmissions, those are, human to human, human to environment, and environment to human. In this paper, a SIRE (Susceptible, Infected, Recovered and Environment of pathogens) epidemic model is proposed and the dynamics of this model is analyzed by both theoretical and numerical means. Firstly, the basic reproduction number (R0 ) which determines whether the disease is extinct or not, is derived. By Routh-Hurwitz criterion theory, we prove that the disease-free equilibrium is unstable and the endemic equilibrium is asymptotically stable when R0 is greater than one. The analysis results are confirmed by some numerical simulations.

KW - Basic reproduction number

KW - Next generation matrix

KW - Rotavirus

KW - Stability analysis

UR - https://www.scopus.com/pages/publications/85092601565

U2 - 10.1063/5.0023487

DO - 10.1063/5.0023487

M3 - Conference contribution

AN - SCOPUS:85092601565

T3 - AIP Conference Proceedings

BT - Symposium on Biomathematics 2019, SYMOMATH 2019

A2 - Apri, Mochamad

A2 - Akimenko, Vitalii

PB - American Institute of Physics Inc.

T2 - Symposium on Biomathematics 2019, SYMOMATH 2019

Y2 - 25 August 2019 through 28 August 2019

ER -

Dynamical behavior of a rotavirus transmission model with an environmental effects

Abstract

Publication series

Conference

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this