The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study

Molalegn Ayana; Tsige Hailegiorgis; Kassahun Getnet

doi:doi:10.11648/j.pamj.20200906.12

| Peer-Reviewed

The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study

Molalegn Ayana, Tsige Hailegiorgis, Kassahun Getnet

Published in Pure and Applied Mathematics Journal (Volume 9, Issue 6)

Received: 23 August 2020 Accepted: 18 September 2020 Published: 23 November 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The COVID−19 pandemic is considered as the biggest global threat worldwide because of millions of confirmed infections, accompanied by hundred thousand deaths over the world. WHO is working with its networks of researchers and other experts to coordinate global work on surveillance, epidemiology, modeling, diagnostics, clinical care and treatment, and other ways to identify, manage the disease and limit onward transmission. Mathematical modeling has become an important tool in analyzing the epidemiological characteristics of infectious diseases. The present study describes the transmission pathways in the infection dynamics, and emphasizes the role of exposed (probably asymptomatic infected) and infected immigrants and the impact of self isolation techniques in the transmission and spread of covid−19 with no home to home check up to develop a mathematical model and show the impact of infected immigrants and self isolation on the dynamics and spread of covid-19. In our model we study the epidemic patterns of Covid−19, from a mathematical modeling perspective. The present model is developed making some reasonable modifications in the corresponding epidemic SCR model by considering symptomatic and asymptomatic infective immigrants as well as self isolation measures. Our numerical results indicate that the corona virus infection would remain pandemic, unless the responsible body takes Self isolation measure and intervention programs and introducing home to home check up of covid−19 to reduce the transmission of the disease from asymptomatic infected (exposed) individual to the susceptible individual. Among the model parameters the exposed and infected self isolation rate and exposed (probably asymptomatic infected) immigration rate are very sensitive parameters for the spread of the virus. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if R₀<1, and unstable if it is R₀>1. Simulation study is conducted using MATLAB ode45.

Published in	Pure and Applied Mathematics Journal (Volume 9, Issue 6)
DOI	10.11648/j.pamj.20200906.12
Page(s)	109-117
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Self Isolation, Home to Home Check Up, Asymptomatic Infected, Symptomatic Infected, Corona Virus Pandemic, Covid-19

References

[1]	Reza Sameni, Grenoble. 19 May 2020. Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus. https://arxiv.org/abs/2003.11371. 19 May 2020.
[2]	Chay Y., Jin Wang. A mathematical model for the novel corona virus pandemic in Wuhan, China. Mathematical Biosciences and Engineering. 11 March 2020.
[3]	Zhi-Qiang, et al. Modeling the Transmission of Middle East Respiratory Syndrome Corona Virus in the Republic of Korea. PLOSONE\|DOI: 10.1371/journal.pone.0144778. December 21, 2015.
[4]	P. van den Driessche, James Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences.
[5]	Novel Coronavirus (2019-nCoV) Situation Report. World Health Organization, 2020.
[6]	B C K Choi, A W P Pak. A simple approximate mathematical model to predict the number of severe acute respiratory syndrome cases and deaths. J Epidemiol Community Health.
[7]	Enahoro Iboi, et. al. Mathematical Modeling and Analysis of COVID-19 pandemic in Nigeria. https://doi.org/10.1101/2020.05.22.20110387. May 22, 2020.
[8]	Meir Shillor, Nofe Al-Asuoad. Mathematical model and simulations of MERS outbreak: Predictions and implications for control measures. ResearchGate. January 2017.
[9]	Lisa E. Gralinskiand Vineet D. Menacher. Return of the Coronavirus: 2019-nCoV. Viruses 2020, 12, 135; doi: 10.3390/v12020135. 24 January 2020.
[10]	Seongwoo Yang et. al. Middle East respiratory syndrome risk perception among students at a university in South Korea, 2015. American Journal of Infection Control.
[11]	Tianmu Chen, et. al. A mathematical model for simulating the transmission of Wuhan novel Coronavirus.. http://dx.doi.org/10.1101/2020.01.19.911669doi. January 19, 2020.
[12]	Demsis Dejene, Purnachandra Rao Koy. Population Dynamics of Dogs Subjected To Rabies Disease. IOSR Journal of Mathematics (IOSR-JM).
[13]	Wendi Wang. Backward Bifurcation of an epidemic model with treatment. Mathematical Bioscience. 8 February 2006.
[14]	Faical Ndairouaet. al. Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan. Center for Research and Development in Mathematics and Applications.
[15]	Benny Yong, and Livia Owen. Dynamical transmission model of MERS-CoV in two area. https://doi.org/10.1063/1.4942993 Published Online: 29 February 2016.
[16]	Molalegn Ayana, Purnachandra Rao Koya. The Impact of Infective Immigrants on the Spread and Dynamics of Zika Virus. American Journal of Applied Mathematics. November 5, 2017.
[17]	Natsuko Imai. et. al. Transmissibility of 2019-nCoV. WHO Collaborating Centre for Infectious Disease Modelling, MRC Centre for Global Infectious Disease Analysis, J-IDEA, Imperial College London, UK. 22/1/20-24/1/20.
[18]	Ning Wang, et. al. An evaluation of mathematical models for the outbreak of COVID-19. Precision Clinical Medicine. doi: 10.1093/pcmedi/pbaa016.
[19]	D. Pal1; D. Ghosh, P. K. Santra, G. S. Mahapatra. Mathematical Analysis of a COVID-19 Epidemic Model by using Data Driven Epidemiological Parameters of Diseases Spread in India. https://doi.org/10.1101/2020.04.25.20079111doi. April 29, 2020.
[20]	Alexander Okhuese Victor. Mathematical predictions for covid-19 as a global pandemic. ResearchGate. https://www.researchgate.net/publication/339944210. 31 March 2020.
[21]	Alex Arenas, et. al. A mathematical model for the spatial temporal epidemic spreading of COVID19. Harvard Medical School & Brigham and Women’s Hospital, Boston MA 02115, US. January 2020.

Cite This Article

Plain Text BibTeX RIS

APA Style

Molalegn Ayana, Tsige Hailegiorgis, Kassahun Getnet. (2020). The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study. Pure and Applied Mathematics Journal, 9(6), 109-117. https://doi.org/10.11648/j.pamj.20200906.12

Copy | Download

ACS Style

Molalegn Ayana; Tsige Hailegiorgis; Kassahun Getnet. The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study. Pure Appl. Math. J. 2020, 9(6), 109-117. doi: 10.11648/j.pamj.20200906.12

Copy | Download

AMA Style

Molalegn Ayana, Tsige Hailegiorgis, Kassahun Getnet. The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study. Pure Appl Math J. 2020;9(6):109-117. doi: 10.11648/j.pamj.20200906.12

Copy | Download

@article{10.11648/j.pamj.20200906.12,
  author = {Molalegn Ayana and Tsige Hailegiorgis and Kassahun Getnet},
  title = {The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study},
  journal = {Pure and Applied Mathematics Journal},
  volume = {9},
  number = {6},
  pages = {109-117},
  doi = {10.11648/j.pamj.20200906.12},
  url = {https://doi.org/10.11648/j.pamj.20200906.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200906.12},
  abstract = {The COVID−19 pandemic is considered as the biggest global threat worldwide because of millions of confirmed infections, accompanied by hundred thousand deaths over the world. WHO is working with its networks of researchers and other experts to coordinate global work on surveillance, epidemiology, modeling, diagnostics, clinical care and treatment, and other ways to identify, manage the disease and limit onward transmission. Mathematical modeling has become an important tool in analyzing the epidemiological characteristics of infectious diseases. The present study describes the transmission pathways in the infection dynamics, and emphasizes the role of exposed (probably asymptomatic infected) and infected immigrants and the impact of self isolation techniques in the transmission and spread of covid−19 with no home to home check up to develop a mathematical model and show the impact of infected immigrants and self isolation on the dynamics and spread of covid-19. In our model we study the epidemic patterns of Covid−19, from a mathematical modeling perspective. The present model is developed making some reasonable modifications in the corresponding epidemic SCR model by considering symptomatic and asymptomatic infective immigrants as well as self isolation measures. Our numerical results indicate that the corona virus infection would remain pandemic, unless the responsible body takes Self isolation measure and intervention programs and introducing home to home check up of covid−19 to reduce the transmission of the disease from asymptomatic infected (exposed) individual to the susceptible individual. Among the model parameters the exposed and infected self isolation rate and exposed (probably asymptomatic infected) immigration rate are very sensitive parameters for the spread of the virus. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if R00>1. Simulation study is conducted using MATLAB ode45.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study
AU  - Molalegn Ayana
AU  - Tsige Hailegiorgis
AU  - Kassahun Getnet
Y1  - 2020/11/23
PY  - 2020
N1  - https://doi.org/10.11648/j.pamj.20200906.12
DO  - 10.11648/j.pamj.20200906.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 109
EP  - 117
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20200906.12
AB  - The COVID−19 pandemic is considered as the biggest global threat worldwide because of millions of confirmed infections, accompanied by hundred thousand deaths over the world. WHO is working with its networks of researchers and other experts to coordinate global work on surveillance, epidemiology, modeling, diagnostics, clinical care and treatment, and other ways to identify, manage the disease and limit onward transmission. Mathematical modeling has become an important tool in analyzing the epidemiological characteristics of infectious diseases. The present study describes the transmission pathways in the infection dynamics, and emphasizes the role of exposed (probably asymptomatic infected) and infected immigrants and the impact of self isolation techniques in the transmission and spread of covid−19 with no home to home check up to develop a mathematical model and show the impact of infected immigrants and self isolation on the dynamics and spread of covid-19. In our model we study the epidemic patterns of Covid−19, from a mathematical modeling perspective. The present model is developed making some reasonable modifications in the corresponding epidemic SCR model by considering symptomatic and asymptomatic infective immigrants as well as self isolation measures. Our numerical results indicate that the corona virus infection would remain pandemic, unless the responsible body takes Self isolation measure and intervention programs and introducing home to home check up of covid−19 to reduce the transmission of the disease from asymptomatic infected (exposed) individual to the susceptible individual. Among the model parameters the exposed and infected self isolation rate and exposed (probably asymptomatic infected) immigration rate are very sensitive parameters for the spread of the virus. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if R00>1. Simulation study is conducted using MATLAB ode45.
VL  - 9
IS  - 6
ER  -

Copy | Download

Author Information

Molalegn Ayana

Department of Mathematics, Dilla College of Teacher Education, Dilla, Ethiopia
Tsige Hailegiorgis

Department of Biology, Kotebe Metropolitan University, Addis Ababa, Ethiopia
Kassahun Getnet

Department of Mathematics, Hawassa University, Hawassa, Ethiopia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Molalegn Ayana, Tsige Hailegiorgis, Kassahun Getnet. (2020). The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study. Pure and Applied Mathematics Journal, 9(6), 109-117. https://doi.org/10.11648/j.pamj.20200906.12

Copy | Download

ACS Style

Molalegn Ayana; Tsige Hailegiorgis; Kassahun Getnet. The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study. Pure Appl. Math. J. 2020, 9(6), 109-117. doi: 10.11648/j.pamj.20200906.12

Copy | Download

AMA Style

Molalegn Ayana, Tsige Hailegiorgis, Kassahun Getnet. The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study. Pure Appl Math J. 2020;9(6):109-117. doi: 10.11648/j.pamj.20200906.12

Copy | Download

@article{10.11648/j.pamj.20200906.12,
  author = {Molalegn Ayana and Tsige Hailegiorgis and Kassahun Getnet},
  title = {The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study},
  journal = {Pure and Applied Mathematics Journal},
  volume = {9},
  number = {6},
  pages = {109-117},
  doi = {10.11648/j.pamj.20200906.12},
  url = {https://doi.org/10.11648/j.pamj.20200906.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200906.12},
  abstract = {The COVID−19 pandemic is considered as the biggest global threat worldwide because of millions of confirmed infections, accompanied by hundred thousand deaths over the world. WHO is working with its networks of researchers and other experts to coordinate global work on surveillance, epidemiology, modeling, diagnostics, clinical care and treatment, and other ways to identify, manage the disease and limit onward transmission. Mathematical modeling has become an important tool in analyzing the epidemiological characteristics of infectious diseases. The present study describes the transmission pathways in the infection dynamics, and emphasizes the role of exposed (probably asymptomatic infected) and infected immigrants and the impact of self isolation techniques in the transmission and spread of covid−19 with no home to home check up to develop a mathematical model and show the impact of infected immigrants and self isolation on the dynamics and spread of covid-19. In our model we study the epidemic patterns of Covid−19, from a mathematical modeling perspective. The present model is developed making some reasonable modifications in the corresponding epidemic SCR model by considering symptomatic and asymptomatic infective immigrants as well as self isolation measures. Our numerical results indicate that the corona virus infection would remain pandemic, unless the responsible body takes Self isolation measure and intervention programs and introducing home to home check up of covid−19 to reduce the transmission of the disease from asymptomatic infected (exposed) individual to the susceptible individual. Among the model parameters the exposed and infected self isolation rate and exposed (probably asymptomatic infected) immigration rate are very sensitive parameters for the spread of the virus. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if R00>1. Simulation study is conducted using MATLAB ode45.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - The Impact of Infective Immigrants and Self Isolation on the Dynamics and Spread of Covid-19 Pandemic: A Mathematical Modeling Study
AU  - Molalegn Ayana
AU  - Tsige Hailegiorgis
AU  - Kassahun Getnet
Y1  - 2020/11/23
PY  - 2020
N1  - https://doi.org/10.11648/j.pamj.20200906.12
DO  - 10.11648/j.pamj.20200906.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 109
EP  - 117
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20200906.12
AB  - The COVID−19 pandemic is considered as the biggest global threat worldwide because of millions of confirmed infections, accompanied by hundred thousand deaths over the world. WHO is working with its networks of researchers and other experts to coordinate global work on surveillance, epidemiology, modeling, diagnostics, clinical care and treatment, and other ways to identify, manage the disease and limit onward transmission. Mathematical modeling has become an important tool in analyzing the epidemiological characteristics of infectious diseases. The present study describes the transmission pathways in the infection dynamics, and emphasizes the role of exposed (probably asymptomatic infected) and infected immigrants and the impact of self isolation techniques in the transmission and spread of covid−19 with no home to home check up to develop a mathematical model and show the impact of infected immigrants and self isolation on the dynamics and spread of covid-19. In our model we study the epidemic patterns of Covid−19, from a mathematical modeling perspective. The present model is developed making some reasonable modifications in the corresponding epidemic SCR model by considering symptomatic and asymptomatic infective immigrants as well as self isolation measures. Our numerical results indicate that the corona virus infection would remain pandemic, unless the responsible body takes Self isolation measure and intervention programs and introducing home to home check up of covid−19 to reduce the transmission of the disease from asymptomatic infected (exposed) individual to the susceptible individual. Among the model parameters the exposed and infected self isolation rate and exposed (probably asymptomatic infected) immigration rate are very sensitive parameters for the spread of the virus. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if R00>1. Simulation study is conducted using MATLAB ode45.
VL  - 9
IS  - 6
ER  -

Copy | Download