nonlinear least-square solvers fmincon  (MathWorks Inc)

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: The values of the parameters used in the SCEAIHR model ( 1 )

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques: Transmission Assay, Modification, Incubation, Infection

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: a and b PRCC indicating sensitivity indices to infected individual ( I ) and basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(R_0)$$\end{document} ( R 0 ) . PRCC values of various parameters with the level of significance 0.05. Sample size = 500 for each parameters is taken based on LHS approach with uniform probability distribution

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques: Infection

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: Contour plots indicating the nature of change in basic reproduction number( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} R 0 ) of SCEAIHR model under parametric planes. a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} R 0 versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ (\rho , \phi _s) \in (0,1]\times (0,0.1]$$\end{document} ( ρ , ϕ s ) ∈ ( 0 , 1 ] × ( 0 , 0.1 ] . b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} R 0 versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\rho , \beta _s) \in (0,1]\times (0,2]$$\end{document} ( ρ , β s ) ∈ ( 0 , 1 ] × ( 0 , 2 ] . (c) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} R 0 versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi _s, \beta _s) \in (0,0.1]\times (0,2]$$\end{document} ( ϕ s , β s ) ∈ ( 0 , 0.1 ] × ( 0 , 2 ]

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques:

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} R 0 versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta ^*$$\end{document} ζ ∗ plot indicating backward bifurcation of SCEAIHR model in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho \in [0.01,0.8]$$\end{document} ρ ∈ [ 0.01 , 0.8 ] . b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} R 0 versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta ^*$$\end{document} ζ ∗ plot illustrating transcritical bifurcation of SCEAIHR model in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _s \in [10\times 10^{-6},2.7\times 10^{-5}]$$\end{document} ϕ s ∈ [ 10 × 10 - 6 , 2.7 × 10 - 5 ] with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho =0$$\end{document} ρ = 0 . All the remaining parameters values are reported in Table

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques:

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: Impacts of variation in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _s$$\end{document} ϕ s , on backward bifurcation with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho \in [0.01,0.8]$$\end{document} ρ ∈ [ 0.01 , 0.8 ] , keeping all parameters value remained same as in Table . The diagram exhibits that the extent of backward bifurcation regime increases gradually with the increasing of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _s$$\end{document} ϕ s

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques:

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: a , b represent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _s$$\end{document} ϕ s versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta ^*$$\end{document} ζ ∗ plot (with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho \in (0,0.1])$$\end{document} ρ ∈ ( 0 , 0.1 ] ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _s$$\end{document} β s versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta ^*$$\end{document} ζ ∗ plot (with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _s \in (0,2])$$\end{document} β s ∈ ( 0 , 2 ] ) . c represent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta ^*$$\end{document} ζ ∗ over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi _s, \beta _s)$$\end{document} ( ϕ s , β s ) matrix plot, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi _s, \beta _s) \in (0.1] \times (0,2]$$\end{document} ( ϕ s , β s ) ∈ ( 0.1 ] × ( 0 , 2 ] . The corresponding color bar indicates values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta ^*$$\end{document} ζ ∗ . The values of the other parameters are taken as same, shown in Table

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques:

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: a , b represent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _s$$\end{document} ϕ s versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$En(\zeta ^*)$$\end{document} E n ( ζ ∗ ) plot (with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _s \in (0,0.1])$$\end{document} ϕ s ∈ ( 0 , 0.1 ] ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _s$$\end{document} β s versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$En(\zeta ^*)$$\end{document} E n ( ζ ∗ ) plot (with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _s \in (0,2])$$\end{document} β s ∈ ( 0 , 2 ] ) . (c) represent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$En(\zeta ^*)$$\end{document} E n ( ζ ∗ ) over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi _s, \beta _s)$$\end{document} ( ϕ s , β s ) matrix plot, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi _s, \beta _s) \in (0,0.1] \times (0,2]$$\end{document} ( ϕ s , β s ) ∈ ( 0 , 0.1 ] × ( 0 , 2 ] . The corresponding color bar indicates values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$En(\zeta ^*)$$\end{document} E n ( ζ ∗ ) . The values of the other parameters are taken as same, shown in Table

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques:

Journal: Nonlinear Dynamics

Article Title: Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

doi: 10.1007/s11071-021-06324-3

Figure Lengend Snippet: Sensitivity indices of the parameters of SCEAIHR model ( 1 ) to I and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} R 0 . \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_i;$$\end{document} I i ; i= 100, 150, 200 th day

Article Snippet: In MATLAB, the nonlinear least-square solver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$fmincon $$\end{document} fmincon has been used during the defined time span to fit the simulated new daily data of COVID-19 recorded by India.

Techniques: