Sensitivity and mathematical model analysis on secondhand smoking tobacco
Abstract In this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single...
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Online Access: | https://doi.org/10.1186/s42787-020-00108-1 |
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doaj-033187ad92f84ab4a0dc2a19af5e7d602020-12-06T12:28:01ZengSpringerOpenJournal of the Egyptian Mathematical Society2090-91282020-12-0128111610.1186/s42787-020-00108-1Sensitivity and mathematical model analysis on secondhand smoking tobaccoBirliew Fekede0Benyam Mebrate1Department of Mathematics, Wollo UniversityDepartment of Mathematics, Wollo UniversityAbstract In this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes.https://doi.org/10.1186/s42787-020-00108-1Secondhand smokerReproduction numberEndemic equilibrium pointSensitivity analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Birliew Fekede Benyam Mebrate |
spellingShingle |
Birliew Fekede Benyam Mebrate Sensitivity and mathematical model analysis on secondhand smoking tobacco Journal of the Egyptian Mathematical Society Secondhand smoker Reproduction number Endemic equilibrium point Sensitivity analysis |
author_facet |
Birliew Fekede Benyam Mebrate |
author_sort |
Birliew Fekede |
title |
Sensitivity and mathematical model analysis on secondhand smoking tobacco |
title_short |
Sensitivity and mathematical model analysis on secondhand smoking tobacco |
title_full |
Sensitivity and mathematical model analysis on secondhand smoking tobacco |
title_fullStr |
Sensitivity and mathematical model analysis on secondhand smoking tobacco |
title_full_unstemmed |
Sensitivity and mathematical model analysis on secondhand smoking tobacco |
title_sort |
sensitivity and mathematical model analysis on secondhand smoking tobacco |
publisher |
SpringerOpen |
series |
Journal of the Egyptian Mathematical Society |
issn |
2090-9128 |
publishDate |
2020-12-01 |
description |
Abstract In this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes. |
topic |
Secondhand smoker Reproduction number Endemic equilibrium point Sensitivity analysis |
url |
https://doi.org/10.1186/s42787-020-00108-1 |
work_keys_str_mv |
AT birliewfekede sensitivityandmathematicalmodelanalysisonsecondhandsmokingtobacco AT benyammebrate sensitivityandmathematicalmodelanalysisonsecondhandsmokingtobacco |
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1724398812783443968 |