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Rehana Naz

Professor, Department of Mathematics & Statistical Sciences

Dr. Naz is a Professor of Mathematics at the Lahore School of Economics, Lahore, Pakistan. She received the M.Sc and M.Phil degrees in Applied Mathematics from Quaid-i-Azam University, Islamabad in 2002 and 2004 and the Ph.D. degree from the University of Witwatersrand, Johannesburg, South Africa in 2008. She was awarded a short-term Post-Doctoral Fellowship from the University of the Witwatersrand, South Africa. Dr. Naz is actively engaged in research, teaching, and academic service. She received the Research Productivity Award from Pakistan Council for Science and Technology in 2012 and was honored with the Best University Teacher Award by Higher Education Commission in Feb 2018.

Dr. Naz has made significant contributions to the subject, her peers and students, the department, the university, and academic and the research community. She has significantly contributed to the designing of several new courses at the Lahore School of Economics. Her teaching portfolio includes Linear Algebra, Calculus, Advanced Calculus, Real Analysis, Mathematical Economics I & II at the undergraduate level, and Mathematical Economics in the M. Phil Economics program. She actively contributed, along with other colleagues from the department, to the development of several minor programs in mathematics and data analytics, launched in 2020. Notably, she played a pivotal role in the development of the BS Double Major in Economics and Mathematics degree program, launched in 2021.

Dr. Naz served on the National Curriculum Revision Committee (NCRC) of the Higher Education Commission (HEC) for curriculum development of BS, MS, and Ph.D. Mathematics. She has been an active member of the Department’s curriculum committee, Board of Studies (BOS), Board of Faculties (BOF), and the academic committee of Lahore School of Economics since October 2009. Dr. Naz is tasked with attending peers' lectures and providing feedback on effective approaches to teaching mathematics. For the faculty at the Lahore school, she has led several training courses on using technology in the classroom, including Zoom, Maple, Python, Latex, Overleaf, Endnote, Mendeley, AI tools and the learning management system of the Lahore School of Economics. She is a reviewer of top Impact factor Journals including Journals published by Sciencedirect, Springer link, Taylor and Francis, IOP. Dr. Naz has worked as the guest editor of many international journals and is working as the Academic Editor of International Journal PLOS ONE. Dr. Naz has presented and worked as an organizer in the several national and international conferences. She was a member of organizing committee of the First Annual Conference on “Mathematical and Statistical Models in Economics, Finance and Applied Sciences” held on February 6-7, 2015 at the Main Campus of Lahore School of Economics. Dr. Naz has organized special sessions in International Conference on Dynamical systems, Differential equations and applications of American institute of Mathematical sciences, held in (Madrid, Spain 7-11 July 2014), (Orlando, Florida, USA 1-5 July 2016), (Taiwan, Taipe 5-9 July 2018) and ( Wilmington, NC USA, May 31 - June 4, 2023).

Dr. Naz has expertise in applying Lie group methods to optimal control theory, calculus of variations, and dynamical systems. She has applied these techniques to a variety of problems arising from physical, biological, and economic phenomena. In her PhD thesis she developed a new theory of constructing conserved quantities for jet flows using conservation laws which is cited by several authors. Most of her research papers have been published in top-ranked world-class journals. She has active research collaboration with professors at leading universities in the USA, UK, Germany, Canada, Italy, Spain, Brazil, Nigeria, and South Africa. Dr. Naz jointly with Dr. Azam Chaudhry and Dr. Fazal Mahomed developed a novel method known as the partial Hamiltonian method for the construction of first integrals for optimal control problems arising in economic growth theory. Closed-form solutions, analyses of the growth rates of capital and consumption, and discussions of saving rates are offered for many celebrated economic growth models to aid policymakers in developing policies. Dr. Naz has supervised several M.Phil Economics students jointly with the leading economist Dr. Azam Chaudhry.

Dr. Naz has published 70 peer-reviewed full-length journal articles, 66 of which are enlisted in the JCR of Web of Science. Notably, her peer-reviewed journal articles include 14 solo-authored, 46 first-authored, 7 second-authored, and 3 third-authored publications. She has also published editorial board notes in the JCR of Web of Science and 4 conference publications. The list of her publications is as follows:

Peer-reviewed full-length research articles in impact factor Journals enlisted in JCR (Web of Science) 

1. Chaudhry, A. Naz, R., (2025). The closed-form solutions for a model with technology diffusion via Lie symmetries, Discrete and Continuous Dynamical Systems -S, 18(4)  1036-1053.
Doi: 10.3934/dcdss.2024133
2. Naz, R. Johnpillai, A, Mahomed, F. M.  Omame, A. Closed-form solutions for a reaction-diffusion SIR model with different diffusion coefficients,  Discrete and Continuous Dynamical Systems – S, 18(4), 870-881.
DOI: 10.3934/dcdss.2024103
3.Naz, R. Torrisi, M. Imran, A. , (2025).  Lie Symmetries and Solutions for a Reaction–Diffusion–Advection SIS Model with Demographic Effects, 17(1), 3.
DOI: https://doi.org/10.3390/sym17010003
4. Naz, R.  Wang, G. Irum, S., (2025).  The closed-form solutions of a diffusive Susceptible-Infectious-Susceptible epidemic model,  Journal of Applied Analysis and Computation, 15 (1), 574-586
DOI: 10.11948/20240175
5. Naz, R. Torrisi, M. (2024). The Closed-Form Solutions of a SIS Epidemic Reaction-Diffusion Model with Advection in a One-Dimensional Space Domain,  SYMMETRY, 16(8), 948.
DOI: https://doi.org/10.3390/sym16080948
6. Naz, R. Johnpillai, A, Mahomed, F. M.  (2024). The exact solutions of a diffusive SIR model via symmetry groups, Journal of Mathematics, Volume 2024, Article ID 4598831, 14 pages.
DOI: https://doi.org/10.1155/2024/4598831
7. Naz, R,. Torrisi, M., (2023). The first integrals and closed-form solutions of a Susceptible-Exposed-Infectious epidemic model, Mathematical Models in the Applied Sciences, 46 (4), 4352-4362. 
DOI: https://doi.org/10.1002/mma.8761
8.Naz, R., & Torrisi, M. (2023). Symmetry methods for a hyperbolic model for a class of populations. Applied Mathematics and Computation, 439, 127640. 
DOI: https://doi.org/10.1016/j.amc.2022.127640
9. Naz, R., & Torrisi, M. (2022). The Transmission Dynamics of a Compartmental Epidemic Model for COVID-19 with the Asymptomatic Population via Closed-Form Solutions. Vaccines, 10(12), 2162.
DOI: https://doi.org/10.3390/vaccines10122162
10. Naz, R. (2022). A current-value Hamiltonian approach to discrete-time optimal control problems in economic growth theory. Journal of Difference Equations and Applications, 28(1), 109-119.
DOI: https://doi.org/10.1080/10236198.2021.2023137
11. Naz, R., & Al?Raeei, M. (2021). Analysis of transmission dynamics of COVID?19 via closed?form solutions of a susceptible?infectious?quarantined?diseased model with a quarantine?adjusted incidence function. Mathematical Methods in the Applied Sciences, 44(14), 11196-11210.
DOI: https://doi.org/10.1002/mma.7481
12. Cheviakov, A., Lee, C., & Naz, R. (2021). Radial waves in fiber-reinforced axially symmetric hyperelastic media. Communications in Nonlinear Science and Numerical Simulation, 95, 105649.
DOI: 10.1016/j.cnsns.2020.105649
13. Naz, R., & Mahomed, F. M. (2021). Hamiltonian symmetry classification, integrals, and exact solutions of a generalized Ermakov system. Mathematical Methods in the Applied Sciences, 44(6), 4467-4478.
DOI: 10.1002/mma.7044
14. Naz, R., & Naeem, I. (2020). Exact solutions of a Black-Scholes model with time-dependent parameters by utilizing potential symmetries. Discrete & Continuous Dynamical Systems-S, 13(10), 2841-2851.
DOI: 10.3934/dcdss.2020122
15. Naz, R. (2020). On sufficiency issues, first integrals and exact solutions of Uzawa-Lucas model with unskilled labor. Discrete & Continuous Dynamical Systems-S, 13(10), 2813-2828.
DOI: 10.3934/dcdss.2020170
16. Naz, R., Mahomed, F. M., & Chaudhry, A. (2020). First integrals of Hamiltonian systems: The inverse problem. Discrete & Continuous Dynamical Systems-S, 13(10), 2829-2840.
DOI: 10.3934/dcdss.2020121
17. Naz, R., & Mahomed, F. M. (2020). Approximate Hamiltonian symmetries and related first integrals. International Journal of Non-Linear Mechanics, 125, art. no. 103547.
DOI: 10.1016/j.ijnonlinmec.2020.103547
18. Naz, R. (2020). Noether-type Hamiltonian symmetry classification, first integrals and exact solutions of two classes of the generalized Ermakov’s systems. The European Physical Journal Plus, 135(8), 641.
DOI: 10.1140/epjp/s13360-020-00631-1
19. Naz, R. (2020). The closed-form solutions for finance-extended Lucas–Uzawa model. Computational and Applied Mathematics, 39(2), 1-29, art. no. 101
DOI: 10.1007/s40314-020-1125-9
20. Naz, R., & Naeem, I. (2019). The approximate Noether symmetries and approximate first integrals for the approximate Hamiltonian systems. Nonlinear Dynamics, 96(4), 2225-2239.
DOI: 10.1007/s11071-019-04893-y
21. Naz, R. (2018). Characterization of approximate Partial Hamiltonian operators and related approximate first integrals. International Journal of Non-Linear Mechanics, 105, 158-164.
DOI: 10.1016/j.ijnonlinmec.2018.06.001
22. Naz, R., & Chaudhry, A. (2018). Closed-form solutions of Lucas–Uzawa model with externalities via partial Hamiltonian approach. Computational and Applied Mathematics, 37(4), 5146-5161.
DOI: 10.1007/s40314-018-0622-6
23. Naz, R., & Johnpillai, A. G. (2018). Exact solutions via invariant approach for Black?Scholes model with time?dependent parameters. Mathematical Methods in the Applied Sciences, 41(12), 4417-4427.
DOI: 10.1002/mma.4903
24. Naz, R., & Mahomed, F. M. (2018). Characterization of partial Hamiltonian operators and related first integrals. Discrete & Continuous Dynamical Systems-S, 11(4), 723-734
DOI: 10.3934/dcdss.2018045
25. Chaudhry, A., & Naz, R. (2018). Closed-form solutions for the Lucas-Uzawa growth model with logarithmic utility preferences via the partial Hamiltonian approach. Discrete & Continuous Dynamical Systems-S, 11(4), 643-654.
DOI: 10.3934/dcdss.2018039 26. Naz, R., & Naeem, I. (2018). The artificial Hamiltonian, first integrals, and closed-form solutions of dynamical systems for epidemics. Zeitschrift für Naturforschung A, 73(4), 323-330.
DOI: 10.1515/zna-2017-0399
27. Naz, R., & Cheviakov, A. F. (2017). Conservation laws and nonlocally related systems of two-dimensional boundary layer models. Zeitschrift für Naturforschung A, 72(11), 1031-1051.
DOI: 10.1515/zna-2017-0238
28. Naz, R., & Chaudhry, A. (2017). Comparison of closed-form solutions for the Lucas-Uzawa model via the partial Hamiltonian approach and the classical approach. Mathematical modelling and analysis, 22(4), 464-483.
DOI: 10.3846/13926292.2017.1323035
29. Chaudhry, A., Tanveer, H., & Naz, R. (2017). Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability. Economic Modelling, 63, 206-214.
DOI: 10.1016/j.econmod.2017.02.009
30. Naz, R. (2017). Potential systems and nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere. Zeitschrift für Naturforschung A, 72(4), 351-357.
DOI: 10.1515/zna-2016-0386
31. Naz, R., & Naeem, I. (2017). Generalization of approximate partial Noether approach in phase space. Nonlinear Dynamics, 88(1), 735-748.
DOI: 10.1007/s11071-016-3273-4
32. Cheviakov, A. F., & Naz, R. (2017). A recursion formula for the construction of local conservation laws of differential equations. Journal of Mathematical Analysis and Applications, 448(1), 198-212.
DOI: 10.1016/j.jmaa.2016.10.042
33. Naz, R. (2016). The applications of the partial Hamiltonian approach to mechanics and other areas. International Journal of Non-linear mechanics, 86, 1-6.
DOI: 10.1016/j.ijnonlinmec.2016.07.009
34. Naz, R., Mahomed, K. S., & Naeem, I. (2016). First integrals and exact solutions of the SIRI and tuberculosis models. Mathematical Methods in the Applied Sciences, 39(15), 4654-4666.
DOI: 10.1002/mma.3903
35. Naz, R., Mahomed, F. M., & Chaudhry, A. (2016). A partial Lagrangian method for dynamical systems. Nonlinear dynamics, 84(3), 1783-1794.
DOI: 10.1007/s11071-016-2605-8
36. Naz, R., Chaudhry, A., & Mahomed, F. M. (2016). Closed-form solutions for the Lucas–Uzawa model of economic growth via the partial Hamiltonian approach. Communications in Nonlinear Science and Numerical Simulation, 30(1-3), 299-306.
DOI: 10.1016/j.cnsns.2015.06.033
37. Naeem, I., Naz, R., & Khan, M. D. (2015). Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems. Zeitschrift für Naturforschung A, 70(12), 1031-1037.
DOI: 10.1515/zna-2015-0072
38. Naz, R., & Mahomed, F. M. (2015). A complex Noether approach for variational partial differential equations. Communications in Nonlinear Science and Numerical Simulation, 27(1-3), 120-135.
DOI: 10.1016/j.cnsns.2015.03.002
39. Naz, R., & Mahomed, F. M. (2015). Dynamic euler-Bernoulli beam equation: classification and reductions. Mathematical Problems in Engineering, 2015. art. no. 520491, . 
DOI: 10.1155/2015/520491
40. Naz, R., Naeem, I., & Mahomed, F. M. (2015). A partial lagrangian approach to mathematical models of epidemiology. Mathematical problems in Engineering, 2015. art. no. 602915, . 
DOI: 10.1155/2015/602915
41. Naz, R., & Mahomed, F. M. (2014). Lie and Noether symmetries of systems of complex ordinary differential equations and their split systems. Pramana, 83(1), 9-20.
DOI: 10.1007/s12043-014-0762-1
42. Naz, R., Freire, I. L., & Naeem, I. (2014). Comparison of different approaches to construct first integrals for ordinary differential equations. In Abstract and applied analysis (Vol. 2014). art. no. 978636, 
DOI: 10.1155/2014/978636
43. Naz, R., Mahomed, F. M., & Chaudhry, A. (2014). A partial Hamiltonian approach for current value Hamiltonian systems. Communications in Nonlinear Science and Numerical Simulation, 19(10), 3600-3610. 
DOI: 10.1016/j.cnsns.2014.03.023
44. Naz, R., Ali, Z., & Naeem, I. (2013). Reductions and new exact solutions of ZK, Gardner KP, and modified KP equations via generalized double reduction theorem. In Abstract and Applied Analysis (Vol. 2013). art. no. 340564, . 
DOI: 10.1155/2013/340564
45. Naz, R., Naeem, I., & Khan, M. (2013). Conservation laws of some physical models via symbolic package GeM. Mathematical Problems in Engineering, 2013, art. no. 897912, . 
DOI: 10.1155/2013/897912
46. Naz, R., Khan, M. D., & Naeem, I. (2013). Conservation laws and exact solutions of a class of non linear regularized long wave equations via double reduction theory and Lie symmetries. Communications in Nonlinear Science and Numerical Simulation, 18(4), 826-834.
DOI: 10.1016/j.cnsns.2012.09.011
47. Naz, R., Khan, M. D., & Naeem, I. (2012). Nonclassical symmetry analysis of boundary layer equations. Journal of Applied Mathematics, 2012, art. no. 938604. 
DOI: 10.1155/2012/938604
48. Naz, R. (2012). Conservation laws for some systems of nonlinear partial differential equations via multiplier approach. Journal of Applied Mathematics, 2012, art. no. 871253 . 
DOI: 10.1155/2012/871253
49. Naz, R. (2012). Conservation laws for laminar axisymmetric jet flows with weak swirl. Applicable Analysis, 91(5), 1045-1052.
DOI: 10.1080/00036811.2011.575367
50. Naz, R. (2012). Conservation laws for some compacton equations using the multiplier approach. Applied Mathematics Letters, 25(3), 257-261.
DOI: 10.1016/j.aml.2011.08.019
51. Naz, R. (2011). Group-Invariant Solutions for Two-Dimensional Free, Wall, and Liquid Jets Having Finite Fluid Velocity at Orifice. Mathematical Problems in Engineering, 2011. art. no. 615612 . 
DOI: 10.1155/2011/615612
52. Mahomed, F. M., & Naz, R. (2011). A note on the Lie symmetries of complex partial differential equations and their split real systems. Pramana, 77(3), 483-491.
DOI: 10.1007/s12043-011-0169-1
53. Naz, R. (2011). Approximate partial Noether operators and first integrals for cubically coupled nonlinear Duffing oscillators subject to a periodically driven force. Journal of Mathematical Analysis and Applications, 380(1), 289-298.
DOI: 10.1016/j.jmaa.2011.02.028
54. Naz, R., Naeem, I., & Mahomed, F. M. (2011). First integrals for two linearly coupled nonlinear Duffing oscillators. Mathematical Problems in Engineering, 2011, art. no. 831647 .
DOI: 10.1155/2011/831647
55. Naz, R., Mason, D. P., & Naeem, I. (2011). Group Invariant Solution for a Liquid Film on the Surface of a Sphere. Zeitschrift für Naturforschung A, 66(5), 272-280.
DOI: 10.1515/zna-2011-0502
56. Naz, R. (2010). Conservation laws for a complexly coupled KdV system, coupled Burgers’ system and Drinfeld–Sokolov–Wilson system via multiplier approach. Communications in Nonlinear Science and Numerical Simulation, 15(5), 1177-1182.
DOI: 10.1016/j.cnsns.2009.05.071
57. Naz, R., Mahomed, F. M., & Hayat, T. (2010). Conservation laws for third-order variant Boussinesq system. Applied Mathematics Letters, 23(8), 883-886.
DOI: 10.1016/j.aml.2010.04.003
58. Naz, R., Naeem, I., & Mahomed, F. M. (2010). Conservation laws and conserved quantities for laminar radial jets with swirl. Mathematical and Computational Applications, 15(4), 742-761.
DOI: 10.3390/mca15040742
59. Naz, R. (2010). Group invariant solution for a free jet on a hemi-spherical shell. Applied mathematics and computation, 215(9), 3265-3270.
DOI: 10.1016/j.amc.2009.10.013
60. Naz, R., Naeem, I., & Abelman, S. (2009). Conservation laws for Camassa–Holm equation, Dullin–Gottwald–Holm equation and generalized Dullin–Gottwald–Holm equation. Nonlinear Analysis: Real World Applications, 10(6), 3466-3471.
DOI: 10.1016/j.nonrwa.2008.09.028
61. Naz, R., Mahomed, F. M., & Mason, D. P. (2009). Conservation laws via the partial Lagrangian and group invariant solutions for radial and two-dimensional free jets. Nonlinear Analysis: Real World Applications, 10(6), 3457-3465.
DOI: 10.1016/j.nonrwa.2008.09.027
62. Naz, R., Mason, D. P., & Mahomed, F. M. (2009). Conservation laws and conserved quantities for laminar two-dimensional and radial jets. Nonlinear Analysis: Real World Applications, 10(5), 2641-2651.
DOI: 10.1016/j.nonrwa.2008.07.003
63. Naz, R., & Mason, D. P. (2009). Conservation Laws for Heated Laminar Radial Liquid and Free Jets. Journal of Nonlinear Mathematical Physics, 16(03), 299-309.
DOI: 10.1142/S1402925109000248
64. Naz, R., Mahomed, F. M., & Mason, D. P. (2008). Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics. Applied Mathematics and Computation, 205(1), 212-230.
DOI: 10.1016/j.amc.2008.06.042
65. Naz, R., Mahomed, F. M., & Mason, D. P. (2008). Symmetry solutions of a third-order ordinary differential equation which arises from Prandtl boundary layer equations. Journal of Nonlinear Mathematical Physics, 15(sup1), 179-191.
DOI: 10.2991/jnmp.2008.15.s1.16
66. Hayat, T., Naz, R., & Asghar, S. (2004). Hall effects on unsteady duct flow of a non-Newtonian fluid in a porous medium. Applied mathematics and computation, 157(1), 103-114.
DOI: 10.1016/j.amc.2003.08.069


Peer-reviewed full-length research articles published in Scopus indexed/other journals

67.    Naz, R. Hereman, W (2025). Lie symmetries, closed-form solutions, and conservation laws of a constitutive equation modeling stress in elastic materials, Partial Differential Equations in Applied Mathematics, 13, 101054, pages 1-10.
Scopus indexed 
DOI: https://doi.org/10.1016/j.padiff.2024.101054
68. Naz, R., Omame, A., Torrisi, M, (2024) Cost-Effectiveness Analysis of COVID-19 Vaccination: A review of some Vaccination Models, Partial Differential Equations in Applied Mathematics. Vol 11, 100842, pages 1-9.
DOI: https://doi.org/10.1016/j.padiff.2024.100842
Scopus indexed 
69. Mahomed, F. M., Mahomed, K. S., Naz, R., & Momoniat, E. (2013). Invariant approaches to equations of finance. Mathematical and Computational Applications, 18(3), 244-250. 
DOI: 10.3390/mca18030244
Scopus indexed
70. Naeem, I., & Naz, R. (2009). Wall jet on a hemi-spherical shell: conserved quantities and group invariant solution. International Journal of Nonlinear Science, 7(2), 149-158.
DOI: IJNS.2009.04.15/212
Editorial board Notes Published in impact factor Journals enlisted in JCR (Web of Science)
71.    Naz, R., Torrisi, M., Freire, I. L., & Naeem, I. (2017). Qualitative and Quantitative Techniques for Differential Equations Arising in Mathematical Physics. Advances in Mathematical Physics, 2017.
DOI: 10.1155/2017/8592571
72. Naz, R., Freire, I. L., Naeem, I., & Torrisi, M. (2014, January). Mathematical methods and models in the natural to the life sciences. In Abstract and Applied Analysis (Vol. 2014), art. no. 706858.
DOI: 10.1155/2014/706858
Conference publications
73.    Naz, R., & Mahomed, F. M. (2018). A Note on the Multiplier Approach for Derivation of Conservation Laws for Partial Differential Equations in the Complex Domain. In Symmetries, Differential Equations and Applications, 266, 125-136,  Springer Proceedings in Mathematics and Statistics, 266, pp. 125-136. 
DOI: 10.1007/978-3-030-01376-9_7    Scopus indexed
74. Naeem, I., Naz, R., & Mahomed, F. M. (2010). First integrals for systems via complex partial Lagrangians. Recent Advances in Bussiness administration, 20-25.
75. Naz, R., Mason, D. P., & Mahomed, F. (2008). Physical conserved quantities for the axisymmetric liquid, free and wall jets. International Journal of Aerospace and Mechanical Engineering, 2(7), 899-903.
76. Naeem, I., & Naz, R. (2008). Group Invariant Solutions for Radial Jet Having Finite Fluid Velocity at Orifice. International Journal of Aerospace and Mechanical Engineering, 2(7), 892-898.