The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss

Molalegn Ayana; Purnachandra Rao Koya

doi:doi:10.11648/j.ajam.20170506.11

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The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss

Molalegn Ayana, Purnachandra Rao Koya

Published in American Journal of Applied Mathematics (Volume 5, Issue 6)

Received: 9 May 2017 Accepted: 27 May 2017 Published: 5 November 2017

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Abstract

In this paper, a compartment model has been built, presented and investigated the dynamics and spread of zika virus in both human and mosquito populations. It is focused to study the impact of symptomatic and asymptomatic infective immigrants on the spread of zika virus. A new mathematical model SI₁I₂R for human and SI model for vector population has been designed and presented. Here I₁ is symptomatic infective and I₂ is asymptomatic infective human populations. The present model is developed making some reasonable modifications in the corresponding epidemic SIR model by considering symptomatic and asymptomatic infective immigrants. Susceptible vectors get infection either from symptomatic or asymptomatic infected human populations. The basic reproduction number is derived using the next generation matrix method. 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 the reproduction number takes a value less than one unit and unstable if it is more than one unit. Simulation study is conducted using MATLAB ode45.

Published in	American Journal of Applied Mathematics (Volume 5, Issue 6)
DOI	10.11648/j.ajam.20170506.11
Page(s)	145-153
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), 2017. Published by Science Publishing Group

Keywords

SI₁I₂R Model, Symptomatic Infected, Asymptomatic Infected, Zika Virus, Microcephally

References

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APA Style

Molalegn Ayana, Purnachandra Rao Koya. (2017). The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss. American Journal of Applied Mathematics, 5(6), 145-153. https://doi.org/10.11648/j.ajam.20170506.11

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ACS Style

Molalegn Ayana; Purnachandra Rao Koya. The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss. Am. J. Appl. Math. 2017, 5(6), 145-153. doi: 10.11648/j.ajam.20170506.11

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AMA Style

Molalegn Ayana, Purnachandra Rao Koya. The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss. Am J Appl Math. 2017;5(6):145-153. doi: 10.11648/j.ajam.20170506.11

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@article{10.11648/j.ajam.20170506.11,
  author = {Molalegn Ayana and Purnachandra Rao Koya},
  title = {The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {6},
  pages = {145-153},
  doi = {10.11648/j.ajam.20170506.11},
  url = {https://doi.org/10.11648/j.ajam.20170506.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170506.11},
  abstract = {In this paper, a compartment model has been built, presented and investigated the dynamics and spread of zika virus in both human and mosquito populations. It is focused to study the impact of symptomatic and asymptomatic infective immigrants on the spread of zika virus. A new mathematical model SI1I2R for human and SI model for vector population has been designed and presented. Here I1 is symptomatic infective and I2 is asymptomatic infective human populations. The present model is developed making some reasonable modifications in the corresponding epidemic SIR model by considering symptomatic and asymptomatic infective immigrants. Susceptible vectors get infection either from symptomatic or asymptomatic infected human populations. The basic reproduction number is derived using the next generation matrix method. 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 the reproduction number takes a value less than one unit and unstable if it is more than one unit. Simulation study is conducted using MATLAB ode45.},
 year = {2017}
}

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TY - JOUR
T1 - The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss
AU - Molalegn Ayana
AU - Purnachandra Rao Koya
Y1 - 2017/11/05
PY - 2017
N1 - https://doi.org/10.11648/j.ajam.20170506.11
DO - 10.11648/j.ajam.20170506.11
T2 - American Journal of Applied Mathematics
JF - American Journal of Applied Mathematics
JO - American Journal of Applied Mathematics
SP - 145
EP - 153
PB - Science Publishing Group
SN - 2330-006X
UR - https://doi.org/10.11648/j.ajam.20170506.11
AB - In this paper, a compartment model has been built, presented and investigated the dynamics and spread of zika virus in both human and mosquito populations. It is focused to study the impact of symptomatic and asymptomatic infective immigrants on the spread of zika virus. A new mathematical model SI1I2R for human and SI model for vector population has been designed and presented. Here I1 is symptomatic infective and I2 is asymptomatic infective human populations. The present model is developed making some reasonable modifications in the corresponding epidemic SIR model by considering symptomatic and asymptomatic infective immigrants. Susceptible vectors get infection either from symptomatic or asymptomatic infected human populations. The basic reproduction number is derived using the next generation matrix method. 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 the reproduction number takes a value less than one unit and unstable if it is more than one unit. Simulation study is conducted using MATLAB ode45.
VL - 5
IS - 6
ER -

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Author Information

Molalegn Ayana

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

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APA Style

Molalegn Ayana, Purnachandra Rao Koya. (2017). The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss. American Journal of Applied Mathematics, 5(6), 145-153. https://doi.org/10.11648/j.ajam.20170506.11

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ACS Style

Molalegn Ayana; Purnachandra Rao Koya. The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss. Am. J. Appl. Math. 2017, 5(6), 145-153. doi: 10.11648/j.ajam.20170506.11

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AMA Style

Molalegn Ayana, Purnachandra Rao Koya. The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss. Am J Appl Math. 2017;5(6):145-153. doi: 10.11648/j.ajam.20170506.11

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@article{10.11648/j.ajam.20170506.11,
  author = {Molalegn Ayana and Purnachandra Rao Koya},
  title = {The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {6},
  pages = {145-153},
  doi = {10.11648/j.ajam.20170506.11},
  url = {https://doi.org/10.11648/j.ajam.20170506.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170506.11},
  abstract = {In this paper, a compartment model has been built, presented and investigated the dynamics and spread of zika virus in both human and mosquito populations. It is focused to study the impact of symptomatic and asymptomatic infective immigrants on the spread of zika virus. A new mathematical model SI1I2R for human and SI model for vector population has been designed and presented. Here I1 is symptomatic infective and I2 is asymptomatic infective human populations. The present model is developed making some reasonable modifications in the corresponding epidemic SIR model by considering symptomatic and asymptomatic infective immigrants. Susceptible vectors get infection either from symptomatic or asymptomatic infected human populations. The basic reproduction number is derived using the next generation matrix method. 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 the reproduction number takes a value less than one unit and unstable if it is more than one unit. Simulation study is conducted using MATLAB ode45.},
 year = {2017}
}

Copy | Download