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Balram Dubey

pilani Mathematics

Professor, Department of Mathematics,
BITS Pilani, Pilani Campus

Mathematical modelling
Department of Mathematics, Birla Institute of Technology & Science, Pilani- 333031, Rajasthan. India.
bdubey@pilani.bits-pilani.ac.in
0091-1596-255660
0091-1596-244183

Scientific Publications

Publications in International Journals

93. Kumar Arjun, Dubey Uma S and Dubey, Balram, Modelling the effect of vaccinations, hospital beds, and treatments on the dynamics of infectious                     disease with delayed optimal control and sensitivity analysis, European Physical Journal Plus, 139: 744, 2024. 

92. Sarif Nawaj, Kumar Arjun, Anshu, Sarwardi Sahabuddin and Dubey Balram, Spatio-temporal dynamics in a delayed prey-predator model with                       nonlinear prey refuge and harvesting, Chaos, Solitons and Fractals, 186: 115247, 2024.

91. Bhargava Masoom and Dubey Balram, Trade-off and chaotic dynamics in a two-prey one-predator model with refuge, environmental noise and                    seasonal effects, Mathematics and Computers in Simulation, 226: 218-245, 2024.

90. Roy Subarna, Sajan, Tiwari Pankaj Kumar and Dubey Balram, Dynamics of a stage-structured predator-prey system with fear-induced group defense           in autonomous and nonautonomous settings, Chaos, 34: 063133, 2024.

89. Anshu, Sajan and Dubey Balram, Bifurcation analysis and spatiotemporal dynamics in a diffusive predator-prey system incorporating a Holling type           II functional response, to appear in International Journal of Bifurcation and Chaos, 34(8): 2450105, 2024.

88. Gupta Ashvini, Sajan and Dubey Balram, Chaos in a seasonal food-chain model with migration and variable carrying capacity, Nonlinear Dynamics,             2024. https://doi.org/10.1007/s11071-024-09718-1.

87. Dubey Balram, Singh Anand and Anshu, Spatio-Temporal Dynamics of Prey-Predator model incorporating Holling-Type II functional response with          fear and its carry-over effects, Chaos, 34: 053108, 2024. https://doi.org/10.1063/5.0203353

86. Sajan, Anshu and Dubey Balram, Study of a cannibalistic prey-predator model with Allee effect in prey under the presence of diffusion, Chaos,                       Solitons and Fractals, 182: 114797, 2024. SCI Journal.

85. Bhargava Masoom, Anshu and Dubey Balram, Spatiotemporal and trade-off dynamics in prey-predator model with domed functional response and             fear effect, International Journal of Bifurcation and Chaos, 34(5): 2450061, 2024. SCI Journal.

84. Kumar Arjun, Dubey Uma S and Dubey, Balram, The impact of radio-chemotherapy on tumour cells interaction with optimal control and sensitivity             analysis, Mathematical Biosciences, 369: 109146, 2024. Scopus Indexed Journal.

83. Kumar Arjun, Dubey Uma S and Dubey, Balram, The impact of social media advertisements and treatments on the dynamics of infectious diseases               with optimal control strategies, Mathematics and Computers in Simulation, 219: 50–86, 2024. SCI Journal.

82. Bhargava Masoom and Dubey Balram, Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense,                         Nonlinear Dynamics, 111: 22727-22761, 2023. SCI Journal. https://doi.org/10.1007/s11071-023-09019-z

81. Pal Soumitra, Gupta Ashvini, Misra A. K. and Dubey Balram, Complex dynamics of a predator-prey system with fear and memory in the presence of            two discrete delays, The European Physical Journal Plus, 138: 984, 2023. SCIE Journal.

80. Anshu and Dubey Balram, Spatio-temporal dynamics of a multi-delayed prey-predator system with variable carrying capacity, Chaos 33: 113116,                   2023. SCI Journal. https://doi.org/10.1063/5.0173566

79. Gupta Ashvini and Dubey Balram, Role reversal in a stage-structured prey-predator model with fear, delay and carry-over effects, Chaos, 33: 093114,           2023. SCI Journal. https://doi.org/10.1063/5.0160222

78. Sajan, Choudhary Kapil Kumar and Dubey Balram, A non-autonomous approach to study the impact of environmental toxins on nutrient-plankton               system, Applied Mathematics and Computation, 458: 128236, 2023. SCI Journal.

77. Kumar Arjun, Gupta Ashvini, Dubey Uma S. and Dubey Balram, Stability and bifurcation analysis of an infectious disease model with different                       optimal control strategies, Mathematics and Computers in Simulation, 213: 78-114, 2023. SCI Journal.

76. Pal Soumitra, Gupta Ashvini, Misra Arvind Kumar and Dubey Balram, Chaotic dynamics of a stage-structured prey-predator system with hunting                 cooperation and fear in the presence of two discrete delays, Journal of Biological Systems, 31(2): 611-642, 2023. SCIE Journal.

75. Bhargava Masoom, Sajan, Dubey Balram, Trade-off and chaotic dynamics of prey–predator system with two discrete delays, Chaos 33, 053120, 2023.          SCI Journal. doi: 10.1063/5.0144182

74. Anshu, Dubey Balram, Sasmal Sourav Kumar and Sudarshan Anand, Consequences of fear effect and prey refuge on the Turing patterns in a delayed          predator-prey system, Chaos 32, 123132, 2022. SCI Journal. https://doi.org/10.1063/5.0126782.

73. Gupta Ashvini and Dubey Balram, Bifurcation and chaos in a delayed eco-epidemic model induced by prey configuration, Chaos, Solitons and                         Fractals, 165: 112785, 2022. SCI Journal.

72. Sajan, Dubey B. and Sasmak S.K., Chaotic dynamics of a plankton-fish system with fear and its carry over effects in the presence of a discrete delay,               Chaos, Solitons and Fractals, 160: 112245, 2022. SCI Journal. https://doi.org/10.1016/j.chaos.2022.112245

71. Gupta Ashvini, Kumar Ankit and Dubey B., Complex dynamics of Leslie-Gower prey-predator model with fear, refuge and additional food under                       multiple delays, Int. J. Biomath., 15(8): 2250060, 2022. SCIE Journal. https://doi.org/10.1142/S1793524522500607

70. Sasmal S.K., Anshu and Dubey B., Diffusive patterns in a predator–prey system with fear and hunting cooperation, Eur. Phys. J. Plus 137:281, 2022.             SCIE Journal. https://doi.org/10.1140/epjp/s13360-022-02497-x

69. Sajan, Sasmal S. K. and Dubey B., A phytoplankton-zooplankton-fish model with chaos control: In the presence of fear effect and an additional food,             Chaos 32: 013114, 2022. SCI Journal. https://doi.org/10.1063/5.0069474

68. Gupta Ashvini and Dubey B., Bifurcations and multi-stability in an eco-epidemic model with additional food, Eur. Phys. J. Plus 137:118, 2022. SCIE               Journal. https://doi.org/10.1140/epjp/s13360-022-02340-3

67. Sajan and Dubey B., Chaos control in a multiple delayed phytoplankton-zooplankton model with group defence and predator's interference, Chaos 31,           083101: 2021. doi: 10.1063/5.0054261. SCI Journal.

66. Dubey P., Dubey Uma S. and Dubey B., Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus           involving total immune response, Nonlinear Analysis: Modelling and Control, 26(4): 678-701, 2021. Scopus Indexed Journal.

65. Dubey B., Sajan and Kumar Ankit, Stability switching and chaos in a multiple delayed prey-predator model with fear effect and anti-predator                           behaviour, Mathematics and Computers in Simulation, 188: 164-192, 2021. SCI Journal.

64. Kumar Ankit and Dubey B., Stability and Bifurcation of a prey-predator system with additional food and two discrete delays, Computer Modeling in               Engineering & Sciences, 126 (2): 505-547, 2021. SCI Journal.

63. Kumar Ankit and Dubey B., Dynamics of prey–predator model with strong and weak Allee effect in the prey with gestation delay, Nonlinear Analysis:             Modelling and Control, 25(3): 417-442, 2020. Scopus Indexed Journal.

62. Kumar Ankit and Dubey B., Modelling the effect of fear in a prey-predator system with prey refuge and gestation delay, International Journal of                       Bifurcation and Chaos, 29(14), 1950195 (25 pages), 2019. SCI Journal.

61. Dubey B. and Kumar Ankit, Dynamics of prey-predator model with stage structure in prey including maturation and gestation delays, Nonlinear                    Dynamics, 96(4), 2653-2679, 2019. DOI: 10.1007/s11071-019-04951-5, SCI Journal.

60. Maiti A.P., Dubey B. and Charaborty A., Global analysis of a delayed stage structure prey-predator model with Crowley-Martin type functional                          response, Mathematics and Computers in Simulation, 162: 58-84, 2019. https://doi.org/10.1016/j.matcom.2019.01.00, SCI Journal.

59. Dubey B., Kumar Ankit and Maiti A. P., Global stability and Hopf-bifurcation of prey-predator system with two discrete delays including habitat                     complexity and prey refuge, Comm. Nonlin. Sci. Numer. Simul., 67: 528-554, 2019. DOI: 10.1016/j.cnsns.2018.07.019, SCI Journal.

58. Dubey B., Agarwal S, and Kumar Ankit, Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage           structure in the predator, Nonlinear Analysis: Modelling and Control, 23(4): 493-514, 2018, SCIE and Scopus Indexed Journal.

57. Dubey Preeti, Dubey Uma S. and Dubey B., Modeling the Role of Acquired Immune Response and Antiretroviral Therapy in the Dynamics of HIV                  Infection, Mathematics and Computers in Simulation, 144:120-137, 2018. https://doi.org/10.1016/j.matcom.2017.07.006, SCI Journal.

56. Maiti A.P. and Dubey B, Stability and bifurcation of a fishery model with Crowley-Martin type functional response, International Journal of Bifurcation         and Chaos, 27 (11), 1750174 (26pages), 2017. SCI Journal.

55. Maiti A.P., Dubey B. and Tushar Jai. A delayed prey-predator model with Crowley-Martin type functional response including prey refuge, Math. Meth.          Appl. Sci., 40(16): 5792-5809, 2017. DOI: 10.1002/mma.4429, SCIE and Scopus Indexed Journal.

54. Thakur N.K., Tiwari S.K., Dubey B. and Upadhyay R.K., Diffusive three species plankton model in the presence of toxic prey: application to Sundarban           mangrove wetland, J. Biol. Systems, 25(2): 185-206, 2017. DOI: 10.1142/S0218339017500103, SCIE and Scopus Indexed Journal.

53. Patra Atasi, Tushar Jai and Dubey B., Modeling and simulation of a wetland park: An application to Keoladeo National Park, India, Mathematics and             Computers in Simulation, 134: 54-78, 2017, SCI Journal. DOI: 10.1016/j.matcom.2016.10.001

52. Lata K., Misra A. K. and Dubey B., Modeling the effects of wood and non-wood based industries on forestry resources, Natural Resource Modelling,              29(4): 559-580, 2016, SCIE Journal.

51. Dubey B., Dubey Preeti and Dubey Uma S., Modeling the intracellular pathogen-immune interaction with cure rate, Comm. Nonlin. Sci. Numer. Simul.,        38: 72-90, 2016. SCI Journal.

50. Deka B.D., Patra Atasi, Tushar Jai and Dubey B., Stability and Hopf-bifurcation in a general Gauss type two-prey and one-predator system, Appl. Math. Model. 40: 5793-5818, 2016, SCIE and Scopus Indexed Journal. http://dx.doi.org/10.1016/j.apm.2016.01.018

49. Dubey B., Dubey Preeti and Dubey Uma S., Role of media and treatment on an SIR model, Nonlinear Analysis: Modelling and Control, 21(2): 185-200,         2015, SCIE and Scopus Indexed Journal.

48. Dubey B., Dubey Preeti and Dubey Uma S., Dynamics of an SIR Model with nonlinear incidence and treatment rate, Appl. Appl. Math., 10(2): 718-737,         2015, MathSciNet(AMS ) Indexed Journal.

47. Dubey B.,, Hussain J., Raw S.N. and Upadhyay R. K., Modeling the effect of pollution on biological species: A socio-ecological problem, Computational        Ecology and Software, 5(2): 152-174, 2015, Web of Science Indexed Journal.

46. Dubey B., Patra Atasi and Sahani S. K., Modelling the dynamics of a renewable resource under harvesting with taxation as a control variable, Appl.                 Appl. Math., 9(2): 592-621, 2014, MathSciNet(AMS) Indexed Journal.

45. Upadhyay R. K., Patra Atasi, Dubey B. and Thakur N. K., A predator-prey interaction model with self- and cross-diffusion in an aquatic systems, J.                 Biol. Systems, Vol. 22, No. 4, 2014, 1450028, 22 pages, SCIE and Scopus Indexed Journal, DOI: 10.1142/S0218339014500284.

44. Dubey B, Patra Atasi and Upadhyay R. K., Dynamics of phytoplankton, zooplankton and fishery resource model, Appl. Appl. Math., 9(1): 217-245,                   2014, MathSciNet(AMS) Indexed Journal.

43. Dubey B., Patra A., Srivastava P.K. and Dubey Uma S., Modeling and analysis of an SEIR model with different types of nonlinear treatment rates, J.               Biol. Systems, Vol. 21, No. 3 (2013) 1350023, 25 pages, SCIE and Scopus Indexed Journal. DOI: 10.1142/S021833901350023X

42. Upadhyay R. K., Naji R. K., Raw S. N., and Dubey B., The role of top predator interference on the dynamics of a food chain model, Communications in           Nonlinear Science and Numerical Simulation, 18(3), 757 – 768, 2013, SCI Journal.

41. Dubey B, and Patra Atasi, A mathematical model for optimal management and utilization of a renewable resource by population, Journal of                              Mathematics, Vol 2013, Article ID 613706, 9 pages, 2013, Scopus Indexed Journal.

40. Dubey B, and Patra Atasi, Optimal Management of a Renewable Resource Utilized by a Population with Taxation as a Control Variable, Nonlinear                  Analysis: Modelling and Control, 18(1), 37-52, 2013, SCIE and Scopus Indexed Journal.

39. Dubey B., Modelling effects of two interacting populations on a renewable resource, Natural Resource Modeling, 25(2), 325 – 363, 2012. DOI:                         10.1111/j.1939-7445.2011.00109.x, SCIE Journal.

38. Dubey B., Dubey Uma S. and Hussain J., Modelling effects of toxicant on uninfected cells, infected cells and immune response in the presence of virus,        J. Biol. Systems, 19(3): 479-503, 2011. DOI: 10.1142/S0218339011004081, SCIE and Scopus Indexed Journal.

37. Dubey B., Zhao T.G., Jonsson M. and Rahmanov H., A solution to the accelerated-predator-satiety Lotka–Volterra predator–prey problem using                    Boubaker polynomial expansion scheme , J. Theor. Biol., 264(1): 154 – 160, 2010, Scopus Indexed Journal. (http://doi:10.1016/j.jtbi.2010.01.026).

36. Dubey B., Shukla J.B., Sharma S., Agarwal A. K. and Sinha P. , A mathematical model for chemical defense mechanism of two competing species,                   Nonlinear Analysis : Real World Applications, 11: 1143 – 1158, 2010, SCI Journal.

35. Upadhyay R.K., Thakur N.K. and Dubey B., Nonlinear non-equilibrium pattern formation in a spatial aquatic system: effect of fish predation, J. Biol.             Systems, 18(1) : 129 – 159, 2010, SCIE and Scopus Indexed Journal.

34. Misra A.K. and Dubey B., A ratio-dependent predator prey model with delay and harvesting, J. Biol . Systems, 18(2): 437 – 453. 2010, SCIE and Scopus         Indexed Journal.

33. Dubey B. and Narayanan A. S., Modelling effects of industrialization, population and pollution on a renewable resource, Nonlinear Analysis : Real                   World Applications, 11: 2833 – 2848, 2010, SCI Journal.  http://dx.doi.org/10.1016/j.nonrwa.2009.10.007 .

32. Dubey B., A model for the effect of pollutant on human population dependent on a resource with environmental and health policy, J. Biol. Systems,               18(3): 571-592, 2010, SCIE and Scopus Indexed Journal. DOI: 10.1142/S0218339010003378

31. Dubey B., Sharma S. Sinha P. and Shukla J.B., Modelling the depletion of forestry resources by population and population pressure augmented                       industrialization, Appl. Math. Model., 13 : 3002-3014, 2009, SCIE and Scopus Indexed Journal.

30. Dubey B, Kumari Nitu, and Upadhyay R.K., Spatiotemporal Pattern formation in a Diffusive Predator-prey system: An analytical approach, J. Appl.               Math. Comp., 31: 413 – 432, 2009, Scopus Indexed Journal.

29. Shukla J. B., Sharma S, Dubey B., and Sinha P., Modeling the survival of a resource dependent population: effects of toxicants (pollutants) emitted                 from external sources as well as formed by its precursors. Nonlinear Analysis : Real World Applications, 10 : 54-70, 2009, SCI Journal.

28. Dubey B., Dubey Uma S. and Banerjee S., Modelling the interaction between avascular cancerous cells and acquired immune response. J. Biol. Systems,         16(3) : 337 – 356, 2008, SCIE and Scopus Indexed Journal.

27. Dubey Uma S. and Dubey B., A mathematical model for the effect of toxicant on the immune system, J. Biol. Systems, 15(4) : 473 – 493, 2007, SCIE               and Scopus Indexed Journal.

26. Dubey B., A prey-predator model with a reserve area, Nonlinear Analysis : Modelling and Control, 12(4) : 479 - 494, 2007, SCIE and Scopus Indexed             Journal.

25. Dubey B. and Hussain J., Modelling the survival of species dependent on a resource in a polluted environment. Nonlinear Analysis : Real – world                   Applications, 7 : 187 – 210, 2006, SCI Journal.

24. Dubey B., A nonlinear model for the topsoil erosion caused by heavy rain, Nonlinear Analysis : Modelling and Control, 10(1) : 35 – 56, 2005, SCIE and           Scopus Indexed Journal.

23. Dubey B., Models for the effect of high speed wind on the depletion of fertile topsoil. Nat. Res. Model. 17(3): 229 – 249, 2004, SCIE Journal.

22. Dubey, B., A model for the effect of time delay on the dynamics of a population living in a polluted environment. J. Biol. Systems, 12(1): 35 – 43, 2004,         SCIE and Scopus Indexed Journal.

21. Dubey B. and Hussain J., Models for the effect of environmental pollution on forestry resources with time delay. Nonlinear Analysis : Real – world                Applications, 5: 549 – 570, 2004, SCI Journal.

20. Dubey B. and Upadhyay R.K., Persistence and extinction of one-prey and two predators system. Nonlinear Analysis : Modelling and Control, 9(4): 1 –           23, 2004, SCIE and Scopus Indexed Journal.

19. Dubey B and Hussain J., Nonlinear models for the survival of two competing species dependent on resource in industrial environments, Nonlinear                Analysis: Theory, Method & Applications (Series B: Real-world Applications),4: 21 – 44, 2003, SCI Journal.

18. Shukla J.B., Agarwal A.K., Sinha P. and Dubey B., Modelling effects of primary and secondary toxicants on renewable resources, Natural Resource                   Modelling, 16(1): 99 - 120, 2003, SCIE Journal.

17. Dubey B., Chandra, P. and Sinha P. , A model for inshore-offshore fishery, J. Biol. Systems, 11(1): 27-42, 2003, SCIE and Scopus Indexed Journal.

16. Dubey B., Chandra, P. and Sinha P., A model for fishery resource with reserve area. Nonlinear Analysis Real-world Applications, 4(4): 625 – 637, 2003,        SCI Journal.

15. Dubey, B., Dynamics of interacting biological species, Comments on Theoretical Biology, 8: 189 – 206, 2003.

14. Dubey B., Upadhaya, R.K. and Hussain, J., Effects of industrialization and pollution on resource biomass: a mathematical model. Ecol Model. 167: 83-
      95, 2003, SCI Journal.

13. Dubey B., Chandra P. and Sinha P., A resource dependent fishery model with optimal harvesting policy, J. Biol. Systems, 10(1) 1-13, 2002, SCIE and               Scopus Indexed Journal.

12. Dubey B., Das B. and Hussain J., A predator-prey interaction model with self and cross-diffusion. Ecol. Model., 141(1-3): 67-76, 2001, SCI Journal.

11. Shukla J. B., Agrawal A. K., Dubey B. and Sinha P., Existence and survival of two competing species in a polluted environment: a mathematical model,          J.  Biological Systems, 9(2): 89-103, 2001, SCIE and Scopus Indexed Journal.

10. Dubey B and Hussain J., Modelling the interaction of two biological species in a polluted environment, J. Math. Anal. Appl., 241(1): 58-79, 2000, SCI            Journal.

9. Dubey B. and Hussain J., A model for allelopathic effect on two competing species, Ecol. Model., 129: 195-207, 2000, SCI Journal.

8. Dubey B. and Das B., Models for the survival of species dependent on resource in industrial environments, J. Math. Anal. Appl., 231: 374-396, 1999, SCI      Journal.

7. The water buffalo controversy in Keoladeo National Park, India-Reply, Ecol. Model., 106(1): 95-98, 1998, SCI Journal.

6. Dubey B., Modelling the depletion and conservation of resources: Effects of two interacting populations, Ecol. Model., 101: 123-136, 1997, SCI Journal.

5. Shukla J. B. and Dubey B., Modelling the depletion and conservation of forestry resource: Effects of population and pollution, J. Math Biol., 36: 71-94,           1997, SCI Journal.

4. Shukla J. B. and Dubey B., Effect of changing habitat on species: Application to Keoladeo National Park, India, Ecol. Model., 86: 91-99, 1996, SCI                   Journal.

3. Shukla A., Dubey B. and Shukla J. B., Effect of environmentally degraded soil on crop yield: The role of conservation, Ecol. Model., 86: 235-240, 1996,             SCI  Journal.

2. Shukla J. B. and Dubey B., Simultaneous effect of two toxicants on biological species: A mathematical model, J. Biol. Syst., 4(1): 91-99, 1996, SCIE and          Scopus Indexed Journal.

1.  Shukla J. B., Dubey B. and Freedman H. I., Effect of changing habitat on survival of species, Ecol. Model., 87(1-3): 205-216, 1996, SCI Journal.

Book Published

  • Introductory Linear Algebra, Asian Books Pvt Ltd, New Delhi, 2007.

 Publications in National Journals

  1.  Dubey B., Das B. and Hussain J., A model for two competing species with self and cross-diffusion, Ind. J. Pure & Appl. Math., 33(6): 847-860, 2002. 
  2.   Dubey B. and Das B., Modelling the interaction of two predators competing for a prey in a diffusive system, Ind. J. Pure & Appl. Math., 31(7): 823-837, 2000.
  3.  Dubey B., Depletion and subsequent conservation of forestry resource biomass: a mathematical model, Proc. Nat. Acad. Sci., India, 68(A) IV: 373-386, 1998.
  4.    Dubey B., A resource based competition model: Effect of population, Far East J. Appl. Math., 1(1): 11-32, 1997.
  5.    Dubey B., Modelling the effect of toxicant on forestry resources, Ind. J. Pure and Appl.Math., 28(1): 1-12, 1997.
  6.    Dubey B. and Das B., Models for the migrating populations in a forested grassland, Far East J. Appl. Math., 1(1): 97-104, 1997. 
  7.    Dubey B., Time delay model for degradation of forestry resources, Ind. J. Ecol., 24 (1): 10-16, 1997. 

Publications in the Proceedings of International Conferences  

  1.   Gupta, A., Dubey, B. (2022). Bifurcation Analysis of a Leslie-Gower Prey-Predator Model with Fear and Cooperative Hunting. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity.  P. 1069–1080. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_90
  2.   Anshu, Sasmal, S.K., Dubey, B. (2022). Impact of Cooperative Hunting and Fear-Induced in a Prey-Predator System with Crowley-Martin Functional Response. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. pp 1015–1026. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_86
  3.  Sajan, Kumar, A., Dubey, B. (2022). Stability Switching in a Cooperative Prey-Predator Model with Transcritical and Hopf-bifurcations. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. pp 987–1000. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_84
  4.  Dubey P., Dubey B. and Dubey Uma S., Optimal control for therapeutic drug treatment on a delayed model incorporating immune response, Proceedings of the International Symposium on Mathematical and Computational Biology, BIOMAT 2015 (Edited by Rubem P Mondaini, Brazil), World scientific, pp. 221-240, June 2016. DOI: http://dx.doi.org/10.1142/9789813141919_0015 
  5.  Dubey P., Dubey B. and Dubey Uma S., An SIR model with nonlinear incidence rate and Holling type III treatment Rate, (Eds.:Cushing, J.M., Saleem, M., Srivastava , H.M., Khan, M.A., Merajuddin, M.), Springer Proceedings in Mathematics and Statistics: Applied Analysis in Biological and Physical Sciences, pp. 63-81, 2016. 
  6.  Dubey B. and Upadhyay R. K., A model for the effect of predation on two competing prey species, Mathematical Biology – Recent Trends (Eds. Peeyush Chandra and B. V. Rathish Kumar),  pp. 242 – 250, 2006.
  7.  Dubey B. and Hussain J., Time delay model for the depletion of forestry resources, Proc. International Conference on Mathematical Modelling, University of Roorkee, India,  616-620, 2001.
  8.  Shukla J. B., Agrwal A. K. and Dubey B., Effects of toxicants (pollutants) on biological species: some mathematical models. In Environmental Stress: Indication, Mitigation and Eco-conservation, M. Yunus, N. Singh and L. J. de Kok (Eds.), 345-356, Kluwer Academics, The Netherlands, 2000.
  9.  Dubey B., Mathematical Models for fishery resources in a polluted marine environment, Proc. International Congress on Environmental Planning and Management, VRCE Nagpur, India, 465-469, 1996.
  10.  Bhattacharya D. K., Reddy Y. H. S. and Dubey B., Multimedia in ecosystems modelling: Application to Keoladeo National Park, India, IASTED (The International Association of Science & Technology for Development) International Conference on Signal and Image Processing and Applications, Annecy, France, June 12-14, 1996, Paper # 241-109.
  11. Shukla J. B., Dubey B. and Agarwal M., Modelling the depletion of forestry resource: Effects of Industrialization and population, Proc. International Congress on Modelling and Simulation, Australia, 2: 845-850, 1993.
  12.  Shukla J. B. and Dubey B., Effects of industrialization and pollution on forest ecosystem, Proc. International Congress on Modelling and Simulation, Australia, 2: 857-862, 1993.
  13.  Shukla J. B., Dubey B. and Shukla A, Sustainable industrial development: A model, Proc. International Congress on Modelling and Simulation, Australia, 2: 997-1004, 1993.

Publications in the Proceedings of National Conferences

  1.  Agarwal A. K., Dubey B., Sinha P. and Shukla J. B., Effects of two or more toxicants on a biological species: a non-linear mathematical model and its analysis, In Mathematical Analysis and Applications, Narosa Publishing House, New Delhi, India, p. 93-109, 2000.
  2.   Shukla J. B., Dubey B. and Shukla A., Effect of two cooperating populations on depletion of forestry resource, Proc. of Recent Trends in Industrial & Applied Mathematics, MACT Bhopal, P. 20-37, 1998.
  3.  Shukla J. B., Agarwal A., Naresh R. and Dubey B., Modelling the removal of pollutants from the atmosphere of an industrial city by monsoon rain, Proc. of Recent Trends in Industrial & Applied Mathematics, MACT Bhopal, p. 184-197, 1998
  4.  Dubey B., Effect of pollutant on biological species: A mathematical model, Proc. of Mathematical Modelling of Ecological and Environmental Systems, Jadavpur University, Calcutta, p. 15-22, 1995.
  5.  Agarwal M., Dubey B. and Shukla J. B., Modelling the depletion of forestry resource: Effects of industrialization and population, Proc. Indian Society of Industrial and Applied Mathematics (ISIAM’92), Roorkee, p. 287-290, 1993.

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