In developing countries, the informal sector plays a crucial role in employing unskilled labor workforce and contributes significantly to economic growth. Informal sector also facilitates skill acquisition, which enhances workers’ employability. This research work presents a dynamical model examining how skilled individuals in the informal sector influence unemployment dynamics. The model considers unemployed persons (both unskilled and skilled) and employed persons as dynamic variables. We analyze the feasibility and stability of all equilibria for the proposed dynamical system. A quantity , analogous to the basic reproductive ratio in epidemic models, is derived. We also demonstrate the existence of various bifurcations, including transcritical, saddle-node, Hopf, and Bogdanov–Takens bifurcations. Additionally, we apply a graph-theoretical approach to analyze unemployment patterns and connections within the labor workforce. This provides insights into the structure and dynamics of unemployment networks, complementing the dynamical system’s analysis. By combining dynamical system’s theory with graph theory, this study provides a comprehensive, multi-dimensional understanding of unemployment dynamics in developing economies characterized by substantial informal sector.
REFERENCES
1.
See https://www.dw.com/en/south-asia-is-facing-an- employment-crisis-unicef-chief/a-51118917 for “South Asia is facing an employment crisis.”
2.
See https://www.undp.org/india/publications/india-skills-report-2019 for “India skills report 2019.”
3.
Times of India, see http://timesofindia.indiatimes.com/business/india-business/articleshow/49107369.cms for “Only 2.2% got formal vocational training NSSO survey.”
4.
M.
Badiuzzaman
and M.
Rafiquzzaman
, “Automation and robotics: A review of potential threat on unskilled and lower skilled labour unemployment in highly populated countries
,” Int. Bus. Manag.
14
(1
), 16
–24
(2020
). 5.
T. F.
Bresnahan
, E.
Brynjolfsson
, and L. M.
Hitt
, “Information technology, workplace organization, and the demand for skilled labor: Firm-level evidence
,” Q. J. Econ.
117
(1
), 339
–376
(2002
). 6.
M.
Goos
, “The impact of technological progress on labour markets: Policy challenges
,” Oxford Rev. Econ. Policy
34
(3
), 362
–375
(2018
). 7.
F.
Bonnet
, J.
Vanek
, and M.
Chen
, Women and Men in the Informal Economy: A Statistical Brief
(International Labour Office
, Geneva
, 2019
), Vol. 20.8.
See https://www.ibef.org/economy/economic-survey-2021-22 for “Economic Survey 2021-22.”
9.
J.
Barber
, “Skill upgrading within informal training: Lessons from the Indian auto mechanic
,” Int. J. Train. Dev.
8
(2
), 128
–139
(2004
). 10.
G.
Carswell
and G.
De Neve
, “Training for employment or skilling up from employment? Jobs and skills acquisition in the Tiruppur textile region, India
,” Third World Q.
45
, 715
–733
(2022
). 11.
M.
Pilz
, G.
Uma
, and R.
Venkatram
, “Skills development in the informal sector in India: The case of street food vendors
,” Int. Rev. Educ.
61
, 191
–209
(2015
). 12.
M.
Ramasamy
and M.
Pilz
, “Competency-based curriculum development in the informal sector: The case of sewing skills training in rural South India
,” Int. Rev. Educ.
65
(6
), 905
–928
(2019
). 13.
I. J.
Regel
and M.
Pilz
, “Informal learning and skill formation within the Indian informal tailoring sector
,” Int. J. Train. Res.
17
(2
), 140
–156
(2019
). 14.
R.
Palmer
, Lifelong Learning in the Informal Economy: A Literature Review
(International Labour Organization
, 2020
).15.
R.
Al-Maalwi
, S.
Al-Sheikh
, H. A.
Ashi
, and S.
Asiri
, “Mathematical modeling and parameter estimation of unemployment with the impact of training programs
,” Math. Comput. Simul.
182
, 05
–720
(2021
). 16.
H. A.
Ashi
, R. M.
Al-Maalwi
, and S.
Al-Sheikh
, “Study of the unemployment problem by mathematical modeling: Predictions and controls
,” J. Math. Sociol.
46
(3
), 301
–313
(2022
). 17.
A.
Galindro
and D. F.
Torres
, “A simple mathematical model for unemployment: A case study in Portugal with optimal control
,” Stat. Optim. Inf. Comput.
6
(1
), 116
–129
(2018
). 18.
L.
Harding
and M.
Neamtu
, “A dynamic model of unemployment with migration and delayed policy intervention
,” Comput. Econ.
51
(3
), 427
–462
(2018
). 19.
A. K.
Misra
and M.
Kumari
, “Dynamic relationship between informal sector and unemployment: A mathematical model
,” Int. J. Bifurcation Chaos
34
(2
), 2450018
(2024
). 20.
A. K.
Misra
and A. K.
Singh
, “A mathematical model for unemployment
,” Nonlinear Anal. Real World Appl.
12
(1
), 128
–136
(2011
). 21.
A. K.
Misra
and A. K.
Singh
, “A delay mathematical model for the control of unemployment
,” Differ. Equ. Dyn. Syst.
21
(3
), 291
–307
(2013
). 22.
A. K.
Misra
, A. K.
Singh
, and P. K.
Singh
, “Modeling the role of skill development to control unemployment
,” Differ. Equ. Dyn. Syst.
30
(2
), 397
–402
(2022
). 23.
S. B.
Munoli
and S. R.
Gani
, “Optimal control analysis of a mathematical model for unemployment
,” Optim. Control. Appl. Methods
37
, 798
–806
(2016
). 24.
S. B.
Munoli
, S. R.
Gani
, and S. R.
Gani
, “A mathematical approach to employment policies: An optimal control analysis
,” Int. J. Stat. Syst.
12
(3
), 549-
–565
(2017
).25.
G. N.
Pathan
and P. H.
Bhathawala
, “Mathematical model for unemployment control a numerical study
,” Int. J. Math. Trends Technol.
49
(4
), 253
–259
(2017
). 26.
T.
Petaratip
and P.
Niamsup
, “Stability analysis of an unemployment model with time delay
,” AIMS Math.
6
(7
), 7421
–7440
(2021
). 27.
A. K.
Singh
, P. K.
Singh
, and A. K.
Misra
, “Combating unemployment through skill development
,” Nonlinear Anal. Model. Control.
25
(6
), 919
–937
(2020
). 28.
A. K.
Misra
and M.
Kumari
, “Modeling the effect of informal and formal jobs on the dynamics of unemployment
,” Int. J. Bifurcation Chaos
34
, 2450116
(2024
). 29.
R.
Bellman
, Introduction to Matrix Analysis
(Society for Industrial and Applied Mathematics
, 1997
).30.
Y. A.
Kuznetsov
, I. A.
Kuznetsov
, and Y.
Kuznetsov
, Elements of Applied Bifurcation Theory
(Springer
, New York
, 1998
), Vol. 112.31.
A. K.
Misra
and J.
Maurya
, “Modeling the importance of temporary hospital beds on the dynamics of emerged infectious disease
,” Chaos
31
(10
), 103125
(2021
). 32.
R. I.
Bogdanov
, “Bifurcation of the limit cycle of a family of plane vector fields/versal deformations of a singularity of a vector field on the plane in the case of zero eigenvalues
,” Sel. Math. Sov.
1
, 373
–387
(1984
).33.
See https://databank.worldbank.org/source/world-development-indicators/preview/on for “World Bank data set.”
34.
F.
Nyabadza
, S.
Mukwembi
, and B. G.
Rodrigues
, “A graph theoretical perspective of a drug abuse epidemic model
,” Physica A
390
(10
), 1723
–1732
(2011
). 35.
F.
Nyabadza
, S.
Mukwembi
, and B. G.
Rodrigues
, “A tuberculosis model: The case of ‘reasonable’ and ‘unreasonable’ infectives
,” Physica A
388
(10
), 1995
–2000
(2009
). 36.
X. F.
Wang
, “Complex networks: Topology, dynamics and synchronization
,” Int. J. Bifurcation Chaos
12
, 885
–916
(2002
). 37.
M. J.
Keeling
and P.
Rohani
, Modeling Infectious Diseases in Humans and Animals
(Princeton University Press
, 2011
).38.
H. I.
Freedman
and J. W. H.
So
, “Global stability and persistence of simple food chains
,” Math. Biosci.
76
(1
), 69
–86
(1985
). 39.
C.
Castillo-Chavez
and B.
Song
, “Dynamical models of tuberculosis and their applications
,” Math. Biosci. Eng.
1
(2
), 361
(2004
). 40.
L.
Perko
, Differential Equations and Dynamical Systems
(Springer Science & Business Media
, 2013
), Vol. 7.© 2025 Author(s). Published under an exclusive license by AIP Publishing.
2025
Author(s)
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