Dr. Mishra is an Assistant Professor in the Department of Engineering Sciences at ABV-IIITM Gwalior, having joined in July 2023. He holds a PhD in Applied Mathematics with a specialization in mathematical biology from NIT Raipur and completed a prestigious ERCIM postdoctoral fellowship at the University of Warsaw. His extensive research background includes tenures at the Norwegian University of Life Sciences, where he specialized in slow-fast dynamical systems and stochastic differential equations applied to sustainable development and biology.

His research focuses on the mathematical modeling of natural and engineering systems through ODEs, PDEs, and stochastic equations, with particular expertise in mathenatical biology. Currently, Dr. Mishra is expanding his research repertoire to include climate modeling and mechanistic digital twin modeling, utilizing numerical simulations to bridge complex mathematical theory with real-world ecological and environmental sustainability.

Note: PhD positions are available at Department of Engineering Sciences (Mathematics/Physics). Contact me if you are interested in mathematical biology, climate modeling.  Applications of PhD are invited in May and November each year. 

Note: I am looking for BTech./MSc. Interns (summer and semster both) with some finantial support to work on research projects in the field of mathematical biology or digital twin development . Interested candidates may directly contact me.

• Assistant Professor Grade-II at Department of Engineering Sciences, ABV-IIITM Gwalior from July 3, 2023 to Till date. 
• Postdoctoral fellow at Faculty of Science and Technology (REALTEK), Norwegian University of Life Sciences NMBU Norway from March 1, 2021 to June 30, 2023.
• ERCIM Postdoctoral fellow at Faculty of Mathematics, Informatics and Mechanics, University of Warsaw Poland from October 1, 2019 to February 28, 2021.

Administrative Positions:

• Assistant Warden (BH-2) from April 2025 to till date. 
• Member of Institutional Standing Purchase Committee from November 2024 to September 2025.
• Departmental DPGC convener from November 2024 to September 2025. 
• Faculty coordinator sports from April 2024 to March 2025.
• Faculty-in-charge sports from July 2023 to April 2024.

Subject Taught: 

• Engineering Mathematics (ES-102)
• Mathematics IV (IMAS-2201)
• Vector Calculus and PDEs (ES-303) 
• Optimization Techniques (ES-306)
• Modeling and Simulation (IMAS-3201)

Postdoctoral Mentorship:

• Dr. Himanshu Jain (Under IGG project)

PhD Supervision: 

• Mr. Adarsh Srivastava (Jointly with Prof. Joydip Dhar from January 2024)
• Ms. Shivani Sharma (Jointly with Dr. Anuwedita Singh from Janurary 2025) 
• Mr. Abhishek Kumar (From January 2025)

UG/PG Supervision: 

• Ms. Megha Yadav (MSc thesis supervision) from Centre for Basic Sciences, PRSU Raipur. 

Publications:

1. P. Mishra. Chemotaxis-driven pursuit-evasion dynamics of a Monod–Haldane-type predator-prey model (Under Review)
2. P. Mishra, M. Yadav, A. Srivastava, B. Tiwari. Emergence of Turing Instability in Schoener-Polis-Holt intraguild predation Model (Under Review).
3. A. Srivastava, P. Mishra*, J. Dhar. Thresholds and Transitions in Climate-Coupled Predator–Prey Models (Under Review)
4. P. Mishra, D. Wrzosek, Global existence for Lotka-Volterra models of predation and competition with diffusion and predator/competitor taxis in the spatial dimension n= 2, 3. Journal of Differential Equations, 47, 113625.  Q1-SCI, MCQ:1.1.
5. P. Mishra, D. Wrzosek, Schoener-Polis-Holt’s model of the intraguild predation with predator taxis and repulsive chemotaxis. Discrete and Continuous Dynamical Systems - Series B, 29 (12) (2024).  https://doi.org/10.0.15.94/dcdsb.2024062. Q1-SCI, MCQ:1.1.
6. P. Mishra, A. Ponossov and J. Wyller. On the dynamics of predator–prey models with role reversal. Physica D: Nonlinear Phenomena (2024): 134100.     https://doi.org/10.1016/j.physd.2024.134100. Q1-SCI, MCQ:1.08
7. P. Mishra, D. Wrzosek, Pursuit-Evasion Dynamics for Bazykin-Type Predator-Prey Model with Indirect Predator Taxis. Journal of Differential Equations 361 (2023)  https://doi.org/10.1016/j.jde.2023.02.063. Q1-SCI, MCQ:2.00.
8. H. Bergland, P. Mishra, P.A. Pedersen, A. Ponossov and J. Wyller. Time delays and pollution in an open access fishery. Natural Resource Modeling (2022), 1-39. https://doi.org/10.1111/nrm.12363. Q2-SCIE, MCQ: 0.13.
9. P. Mishra and D. Wrzosek. Repulsive chemotaxis and predator evasion in predator prey models with diffusion and prey taxis. Mathematical Models and Methods in Applied Sciences 32 (2022), 1-42. https://doi.org/10.1142/S0218202522500014. Q1-SCI, MCQ: 2.77.
10. P. Mishra and D. Wrzosek. Indirect taxis drives spatio-temporal patterns in an extended Schoener’s intraguild predator-prey model. Applied Mathematics Letters 125 (2021), 107745.  https://doi.org/10.1016/j.aml.2021.107745. Q1-SCI, MCQ:1.17.
11. Mishra and B. Tiwari. Drivers of pattern formation in a predator-prey system with defense in fearful prey. Nonlinear Dynamics 105 (2021).  https://doi.org/10.1007/s11071-021-06719-2. Q1-SCI, MCQ:0.81.
12.  S.N. Raw, P. Mishra, B. Tiwari. B.P. Sarangi. Appearance of temporal and spatial chaos in an ecological system: A Mathematical Modeling Study. Iranian Journal of Science and Technology, Transactions A: Science 45 (2021) SCI https://doi.org/10.1007/s40995-021-01139-8. Q2-SCIE, MCQ: 0.21.
13. S.N. Raw and B. Tiwari and P. Mishra. Qualitative analysis of a predator-prey system with double Allee effect and schooling behaviour. Nonlinear Dynamics 102(10)(2020). SCI. https://doi.org/10.1007/s11071-020-06018-2.Q1-SCI, MCQ:0.81.
14. S.N. Raw and B. Tiwari and P. Mishra. Analysis of a plankton-fish model with external toxicity and non-linear harvesting. Ricerche Da Mathematica Vol. 69 (2020). SCIE. https://doi.org/10.1007/s11587-019-00478-4. Q3-SCIE, MCQ: 0.37.
15. P. Mishra, S.N. Raw, B. Tiwari. On the dynamics of a cannibalistic predator-prey model with defense and diffusion. Applied Mathematical Modelling 90 (165-190) (2020). SCIE https://doi.org/10.1016/j.apm.2020.08.060. Q1-SCIE, MCQ:0.27.
16.  S.N. Raw and P. Mishra, B. Tiwari, Mathematical study about a predator-prey model with anti-predator behavior. International Journal of Applied and Computational Mathematics Vol. 6 (1-22) (2020).  https://doi.org/10.1007/s40819-020-00822-5. Scopus,  MCQ:0.17. 
17. P. Mishra and D. Wrzosek. The role of indirect prey-taxis and interference among predators in pattern formation. Mathematical Methods in Applied Sciences Vol. 43(18) (2020). SCIE https://doi.org/10.1002/mma.6426. Q2-SCIE, MCQ: 0.73.  
18. S.N. Raw and B. Tiwari and P. Mishra. Dynamical complexities and pattern formation in an eco-epidemiological model with prey infection and harvesting. Journal of Applied Mathematics and Computing. Vol. 64 (17-52) (2020). SCIE https://doi.org/10.1007/s12190-020-01342-715. Q2. SCIE-MCQ: 0.67.
19. P. Mishra, S.N. Raw and B. Tiwari. Study of a diffusive Leslie-Grower predator-prey system with mutual interference of predators and prey defense. Chaos, Solitons and Fractals. Vol. 120 (2019). SCI https://doi.org/10.1016/j.chaos.2019.01.012. Q1. SCI, MCQ: 0.54.
20. P. Mishra, S.N. Raw. Dynamical complexities in a predator-prey model involving team of two prey and one predator. Journal of Applied Mathematics and Computing. Vol. 61 (1-2) (2019) ,SCIE https://doi.org/10.1007/s12190-018-01236-. Q2. SCIE-MCQ: 0.67.
21. S.N. Raw and P. Mishra. Modeling and analysis of inhibitory effect in the plankton-fish model: Application to Swarjedski Lake, Western Poland. Nonlinear Analysis: Real World Application. Vol. 46 (2019). SCI https://doi.org/10.1016/j.nonrwa.2018.09.026. Q1. SCIE-MCQ: 1.41.
22. S.N. Raw, P. Mishra, R. Kumar, S. Thakur. Complex dynamics of prey-predator system exhibiting group defense: A mathematical modeling study. Chaos, Solitons and Fractals. Vol. 100 (2017). SCI https://doi.org/10.1016/j.chaos.2017.05.010. Q1. SCI, MCQ: 0.54.

Grants and Funding:

1. Sponsored research project grant of GBP 13506/- (appox. Rs. 16.2 lakh) to work on project "Modeling extreme weather  events in fishery dynamics" (Sep 2025, Feb 2027, PI) from International Growth Centre, United Kingdom.
2. Sponsored research project grant for project "Conceptual mathematical modeling for ecological sustainability" of NOK 37,400 (approx. 3.36 lakh) (Dec 2024-Dec 2025, PI) from NMBU Norway. 
3. FIG grant of INR 9.74 Lakhs for two years from ABV-IIITM Gwalior. (Nov 2023-Nov 2025)
4. International travel grant of NOK 195000 (approx. Rs. 17.55 lakh) from the Norwegian University of Life Sciences NMBU Norway for the research exchange stay in the University of Leicester, UK during July, 2023-November 2023.
5. Travel grant of NOK 25800 (approx. Rs. 2.32 lakh) from Norwegian University of Life Sciences Norway to attend the Third International Nonlinear Dynamics Conference (NODYCON 2023), organized by Sapienza University of Rome, Italy June 18-22, 2023
6. Partial funding (80 Euro/Diem) for 4 day stay at Erwin Schrödinger International Institute for Mathematics and Physics (ESI) of the University of Vienna to participate in the Kyoto-Vienna Workshop of the Thematic Programme on “Mathematical Methods for the Study of Self-organization in the Biological Sciences” from December 1 to 2, 2022.
7. Research exchange (with Inria Dracula Team) funding to 1 week stay upto 1500 Euro (Approx. Rs. 1.56 lakh) by ERCIM - the European Research Consortium for Informatics and Mathematics (not availed due to Covid-19 restrictions)
8. ERCIM Alain Bensoussan Grant of Euro 25360/- (approx. Rs. 26.42 lakh) from 2019-2021 to work on project "The role of chemical signalling and animal's aggregation in predator-prey interactions: Mathematical modelling approach" at University of Warsaw, Poland. 

Conferences and Workshops Organised:

1. ANRF Sponsored International Conference on Mathematical and Computational Frontiers for Sustainable Development (MATHSD 2025), October 16-17, 2025. 
2. TIIC Sponsored 1-Day workshop on Crafting Innovative Startups from Reearch Excellence, May 10 2025. 
3. Self Sponsored International Workshop on Mathematical Models and Methods in Life Sciences, May 15-18, 2024.

Selected Invited and Conference Talks:

1. INVITED TALK entitled “Theory, Numerics, and Application of Reaction-Diffusion Systems” at 5-Day Workshop on Numerical and Machine Learning Techniques in Applied Mathematics (NMAM) -2025, NIT Jamshedpur
2. INVITED TALK entitled “Modeling and Simulation of Bio- inspired Reaction-Diffusion Systems” at National Level Short-Term Training Programme (STTP) on “Frontiers in Applied Mathematics: Modelling, Computation, and Quantum-Driven Techniques (FAMMCQDT-2025), NIT Raipur.
3. INVITED TALK entitled " Mathematical Framework for Pattern Formation in Biology" at the 3rd International Workshop on Advanced Topics in Mathematics. (IWATM-2024), organized at International Institute of Information Technology, Naya Raipur (IIIT-NR). 
4. CONTRIBUTED TALK entitled "Role of repulsion in predator-prey models" in International Conference on Emerging Frontiers in Mathematical and Computational Sciences (EFMCS-2024, held at North-Eastern Hill University (NEHU) Shillong, Meghalay, 24-26 October 2024.
5. CONTRIBUTED TALK entitled "Chemical Signalling and Pattern Formation in Predator-Prey Models" at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) in Waseda University, Tokyo, Japan August 20-25, 2023.
6. INVITED TALK entitled " Chemotaxis and Pattern Formation in Ecological Models" at International seminar on Mathematical Modeling and Turing Pattern Formation organized at School of Advanced Sciences, VIT Vellor India. September 11-15, 2023.
7. CONTRIBUTED TALK entitled "Chemical Signalling and Pattern Formation in Schoener’s Predator–Prey Model" at the Third International Nonlinear Dynamics Conference (NODYCON 2023) in Sapienza University of Rome, Rome, Italy. June 18-22, 2023
8. CONTRIBUTED TALK entitled " Modelling chemical signalling and chemotaxis in predator-prey systems" in the National Symposium on Implementation and Applications of Mathematics in Real Life held at VIT Vellore (iMPLEMATHATION 2023), 8-12th May 2023.
9. CONTRIBUTED TALK entitled "The role of indirect predator-taxis in an extended Schoener’s intraguild predator-prey model " during the 13th DSABNS 2022 conference at the Basque Center for Applied Mathematics (BCAM) and held on February, 8-11, 2022 (Virtual).
10. INVITED talk on "Application of Mathematics in Ecological Sustainability" in the five days webinar from on the theme, “Industrial Mathematics and Scientific Computing” at the Department of Mathematics, BMSIT& M, Bengaluru on 10th January 2022 (Virtual)
11. Virtual talk on "The role of indirect prey-taxis and interference among predators in pattern formation" at RUDN University Russia on 11 February 2021.
12.  Contributed Talk on "Pattern formation in a predator-prey model with defence in fearful prey " at a virtual international conference "Dynamics of biological systems: from viruses to populations" organized by Jagiellonian University, Kraków Poland on 25 September 2020
13. INVITED TALK entitled " Nonlinear Differential Equations and its Application" at Teerthanker Mahaveer University, Moradabad, India on 16 June 2020 (Online)
14. Given a talk on "Role of indirect-prey taxis and mutual interference among predator in pattern formation" at the Institute of Applied Mathematics and Mechanics, University of Warsaw Poland on 10 June 2020.