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

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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

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

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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.

DOI	10.11648/j.pamj.20200906.12
Published in	Pure and Applied Mathematics Journal (Volume 9, Issue 6, December 2020)
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), 2024. Published by Science Publishing Group

Keywords

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

References

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[18]	Ning Wang, et. al. An evaluation of mathematical models for the outbreak of COVID-19. Precision Clinical Medicine. doi: 10.1093/pcmedi/pbaa016.
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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

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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

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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

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@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}
}

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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  -

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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

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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

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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

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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

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@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  -

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