American Journal of Applied Mathematics
Volume 5, Issue 6, December 2017, Pages: 145-153
Received: May 9, 2017;
Accepted: May 27, 2017;
Published: Nov. 5, 2017
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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
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.
Purnachandra Rao Koya,
The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss, American Journal of Applied Mathematics.
Vol. 5, No. 6,
2017, pp. 145-153.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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Ebeneza. B, Kazem Oake. O. 2016. Mathematical modeling of Zika virus. Asian Pacific Journal of Tropical Disease. Sep 2016.
Raúl Isea, Karl E. Lonngren. A Preliminary Mathematical Model for the dynamic Transmission of Dengue, Chikungunya and Zika. American Journal of Modern Physics and Application. 24 June, 2016.
Victor M., Baltazar E., Derdei B., Susan A. Holechek, and Carlos C. Simon. Role of short-term dispersal on the dynamics of Zika virus. Center for Infectious Diseases and Vaccinology, the Biodesign Institute, Arizona State University 16 Mar 2016.
Nidhi Nirwani, V. H. Badshah, R. Khandelwal. A Mathematical Model of Malaria Disease with Vertical Transmission. Published by Canadian Center of Science and Education. 7 August 2015.
Mary K. K., Tomas Allen, Veronika Frank, Ravi S. Santhana, Christopher D. The origin and spread of a mosquito-borne virus. Bulletin of the World Health Organization. 9 February 2016.
T. Alex Perkins, Amir S S., Corrine W. R., Moritz U. G. Kraemer, Andrew J. Tatem. Model based projections of Zika virus infections in childbearing women in the America. 12 Feb.2016 http://dx.doi.org/10.1101/039610.
Maimuna S M., Emily C., Durland F., John S. Estimating a feasible serial interval range for Zika fever. Bulletin of the World Health Organization. 9 February 2016.
Abadi Abay Gebremeskel, Harald Elias Krogstad. Mathematical Modeling of Endemic Malaria Transmission. American Journal of Applied Mathematics. 12 February 2015.
Mikayla C. Chubb Kathryn H. J. Mathematical modeling and the epidemiological research. European Journal of Epidemiology. 27 October 2009.
S. Olaniyi, O. S. Obabiyi. Mathematical model for malaria transmission dynamics in human and Mosquito populations with non-linear force of infection. International Journal of Pure and Applied Mathematics. 15 August 2013.
Syafruddin Side, Salmi Md Noorani. A SIR Model for Spread of Dengue Fever Disease. World Journal of Modeling and Simulation. 14 April 2013.
Zika virus fact sheet. Ethiopian midwives association.
Epidemiological alert. Neurological syndrome, congenital malformations, and Zika virus infection. Implications for public health in the Americas. Pan American Health Organization (PAHO) / World Health Organization (WHO). 1 December 2015.
Katherine F. D., Alexa O., Emily P. Interim Zika Virus Clinical Guidance and Recommendations. Centers for Disease Control and Prevention. 26 January, 2016.
Rapid Risk Assesment, Zika virus disease epidemic: potential association with microcephaly and Guillain-Barré syndrome. 20 January 2016.
Thais D. S, Wanderson K. D. Zika Virus and the Guillain-Barre Syndrome: Case Series from Seven Countries. The new England journal of medicine. 20 October 2016.
Sandip M., Ram R. S, and Somdatta S. Mathematical models of malaria. Mandal et al. Malaria Journal (2011, 10: 202).
Kelly A. T. Benign bacteria block mosquitoes from transmitting Zika, chikungunya viruses. University of Wisconsin U Madison. 1 Jun 2016.
Tadele Tesfa Tegegne, Purnachandra Rao Koya, Temesgen Tibebu Mekonnen. Impact of Heterosexuality and Homosexuality on the transmission and dynamics of HIV/AIDS. IOSR Journal of Mathematics. Dec. 2016. e-ISSN: 2278 - 5728, p-ISSN: 2319 - 765X. Volume 12, Issue 6 Ver. V (Nov. - Dec.2016), PP 38-49 www.iosrjournals.org.
Iurii Bakach. A survey of mathematical models of Dengue fever. Georgia Southern University, electronic thesis and dissertation.
Yingyun Shen. Mathematical Models of Dengue Fever and Measures to Control It. Florida State University Libraries, Electronic Theses, Treatises and Dissertations. Semester, 2014.