I am an independent researcher with no formal affiliation to any academic institution or research lab. I conduct research purely driven by my own interests and with self-sourced funding. My passion lies in the realm of studying and conducting research, which fuels my deep love for the pursuit of knowledge. I am particularly keen on collaborating with others on research projects related to mathematical modeling in areas such as biology, sociology, and real-world problem-solving, among others.
EDUCATION
M.Sc. (Mathematics) from Indian Institute of Engineering Science and Technology, Shibpur: Howrah, West Bengal, INDIA
PhD (Mathematics) from Maulana Abul Kalam Azad University of Technology: Kolkata, West Bengal, INDIA
RESEARCH, TEACHING, or OTHER INTERESTS
Applied Mathematics, Modeling and Simulation, Multidisciplinary
Global stability and sensitivity analysis of dengue transmission using four host and three vector classes along with control strategies R. Prem Kumar, G.S. Mahapatra, Sanjoy Basu, P.K. Santra International Journal of Computer Mathematics, 2026 This study of stability and optimal control has exhibited essential facts of the interaction of four host and three vector populations to determine the biological viability of the proposed dengue virus transmission model. This presents a sensitivity analysis of the threshold parameter value R0 and conditions determining the persistence of the disease. The local and global stability analysis is performed using the threshold parameter on disease-free and endemic equilibrium points. The analytical solution shows its optimal effect on the spread of the disease and is supported by numerical simulations, which recommend implementing appropriate control measures to stop the dengue virus from transmitting from infected mosquitoes to humans. The model validation is carried out using actual infected human cases, and the suggested model shows strong agreement with the observed data, highlighting its accuracy and dependability. This analysis could prove crucial for health authorities trying to stop the spread of dengue fever.
Price-dependent fuzzy demand and shortages scenario with memory effect on inventory system incorporating optimal replenishment strategy Shilpi Pal, P K Santra, G S Mahapatra Engineering Research Express, 2025 This paper develops an optimal replenishment strategy with indeterminate demand predisposed by the item’s price. The study uses a Caputo-fractional differential equation to discuss how the memory sequel is created in the customer’s mind regarding sales pattern formulation. As the customer’s purchase pattern can’t be predicted initially, this research incorporates the triangular fuzzy in price-dependent demand and the effect of unforeseen shortages. This study provides the decisive scheme for determining the optimal number of cycles along with an estimated refilling time to attain minimal total expense and the memory effect of the customer. A numerical study under the numerical data from a retail store’s empirical findings, if the ordering of items is increased by 15% then the retailer’s cost is increased by approximately 5%. This result supports the sales strategy managerial belief that retailers must order more items to avoid stockouts owing to demand uncertainty.
DYNAMICAL ANALYSIS OF DISPERSAL IMPACT ON A THREE-PATCH BASED PREDATOR-PREY SYSTEM WITH STRONG ALLEE EFFECTED PREYS S. Biswas, D. Pal, P.K. Santra, G. S. Mahapatra Mathematics in Applied Sciences and Engineering, 2025 This paper describes a three-patch based predator-prey interaction model where a strong Allee effect accomplishes each prey species in their respective patches. It is also assumed that only the prey species are movable among the patches following the balanced dispersal rule. The stability behavior at the inner equilibrium point has been studied in the presence and non-existence of dispersal. This study also observes a vital characteristic of the Allee edge regarding the stability of the equilibrium of the model when prey species progress freely in their patches. Also, the dispersal can destabilize the interior equilibrium of populations, i.e., if the interior equilibrium becomes unstable in the absence of dispersal under some conditions, it becomes stabilized under some conditions whenever the prey species move among their patches. The Hopf bifurcation behavior of the system has been studied and numerical simulations have been performed taking hypothetical parameter values using MATHEMATICA and MATLAB software.
LEARNING AND MEMORY EFFECT IN A FRACTIONAL ORDER QUANTITY MODEL INCORPORATING PROMOTION-ASSISTED DEMAND UNDER UNCERTAINTY Arup Dasgupta, Amalendu Singha Mahapatra, Prasun Kumar Santra, Ghanshaym Singha Mahapatra, Ashok Kumar Shaw, Biswajit Sarkar Journal of Industrial and Management Optimization, 2024 In supply systems, maintaining stock levels is a major challenge. The purpose of this article is to determine the number of orders in a continuous review model. The demand rate is erratic, as it is dependent on promotional advertising on an ambiguous basis. This article considers learning and memory in an unpredictable setting. The fundamental crisp model is extended with a fuzzy formulation, and learning is included. Demand promotion is included with the complete backlog in models, which are based on finite-horizon time scales. The memory present in real-world situations is represented using Caputo's style of nonintegral ordered calculus. It focuses on the percentage of each process that is devoid of scarcity as well as the overall cycles of replenishment. After analyzing each model numerically, a parametric sensitivity analysis is performed to show the trade-offs and efficacy of the decision criteria. Longer memory and higher learning rates have been found to result in a cheaper total cost. The number of fuzzy learning orders and the overall cost shift in an inversely proportionate manner as learning increases.The fuzzy learning case's total cost decreases rather than the fuzzy case's if the differential fractional order rises within the range. The crisp model, which derives minimal total cost, is relevant as a mathematical bound for the other two realistic models that incorporate demand volatility and are the main goals of this simulation. These models ameliorate the burden of implausibly perfect demand knowledge. This simulation is used to analyze the increases in the inventory system's output for each model. With learning, the inventory and total cost are less than those of a pure fuzzy system: the fuzzy model's delta over the crisp limiter is reclaimed by 62% for the order size and by 39% for the cost over the considered horizon. This accurately simulates how experience leads to better decision-making. A move to shorter memory has twin manifestations in order size: differential memory index generates linear reduction with a mean rolling fall of 10.5% per 0.1 change but the integral index causes a stronger (20%) quadratic reduction. For the total cost, their roles are reversed: both cause quadratic increase with shorter memory but the differential index has the stronger impact - a mean rolling rise of 11% per 0.1 change compared to 6.5% for the integral index.
Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response Md. Jasim Uddin, P. K. Santra, Sarker Md Sohel Rana, G.s. Mahapatra Chaos Theory and Applications, 2024 This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point.
IMPACT OF FEAR AND HARVESTING EFFORT ON A DIFFERENTIAL-ALGEBRAIC PREY-PREDATOR MODEL BASED ON SQUARE ROOT FUNCTIONAL RESPONSE AA Elsadany, GS Mahapatra, PK Santra, D Pal, A Elsonbaty, ... Journal of Mathematical Sciences 298 (1), 37-57 , 2026 2026 Citations: 2
Global stability and sensitivity analysis of dengue transmission using four host and three vector classes along with control strategies R Prem Kumar, GS Mahapatra, S Basu, PK Santra International Journal of Computer Mathematics 103 (1), 1-26 , 2026 2026 Citations: 4
Dynamics under interactive delay in the predator of a three-species system with impreciseness and strong Allee effect in the prey S Biswas, GS Mahapatra, D Pal, PK Santra International Journal of Modelling and Simulation, 1-23 , 2025 2025
Modeling three compartmental voter dynamics for a multiparty state electoral system R Induchoodan, PK Santra, GS Mahapatra Journal of Dynamics and Games, 0-0 , 2025 2025
Price-dependent fuzzy demand and shortages scenario with memory effect on inventory system incorporating optimal replenishment strategy S Pal, PK Santra, GS Mahapatra Engineering Research Express 7 (2), 025433 , 2025 2025
Dynamical analysis of dispersal impact on a three-patch based predator-prey system with strong Allee effected preys S Biswas, D Pal, PK Santra, GS Mahapatra Mathematics in Applied Sciences and Engineering 6 (2), 94-124 , 2025 2025
Dynamical study of discrete prey-predator system incorporating proportional prey refuge with interval parameters PK Santra, GS Mahapatra Applied Mathematics-A Journal of Chinese Universities 40 (2), 276-296 , 2025 2025
Control strategies on a two-serotype dengue transmission model with saturated incident function RP Kumar, GS Mahapatra, PK Santra International Journal of Dynamics and Control 13 (6), 227 , 2025 2025
Dynamical analysis of SARS-CoV-2-Dengue co-infection mathematical model with optimum control and sensitivity analyses RP Kumar, GS Mahapatra, PK Santra Nonlinear Analysis: Real World Applications 80, 104175 , 2024 2024 Citations: 9
Learning and memory effect in a fractional order quantity model incorporating promotion-assisted demand under uncertainty A Dasgupta, AS Mahapatra, PK Santra, GS Mahapatra, AK Shaw, ... Journal of Industrial and Management Optimization 20 (11), 3514-3551 , 2024 2024 Citations: 3
Optimal control model for IVF treatment in women B Yeolekar, N Shukla, J Shukla, M Yeolekar, S Patil, PK Santra International Journal of Biomathematics, 2450101 , 2024 2024 Citations: 2
Optimal control for dengue transmission based on a model with reinfection and treatment RP Kumar, GS Mahapatra, PK Santra, JJ Nieto Mathematical Population Studies 31 (3), 165-203 , 2024 2024 Citations: 8
Analyzing election trends incorporating memory effect through a fractional-order mathematical modeling PK Santra, I R, GS Mahapatra Physica Scripta 99 (7), 075239 , 2024 2024 Citations: 5
Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact PK Santra, GS Mahapatra, S Basu Physica Scripta 99 (6), 065237 , 2024 2024 Citations: 2
Global stability and sensitivity analysis of parameters of Omicron variant epidemic in diverse susceptible classes incorporating vaccination stages: R. Prem Kumar et al. R Prem Kumar, S Basu, PK Santra, AA Elsadany, A Elsonbaty, ... Soft Computing 28 (6), 4689-4713 , 2024 2024 Citations: 11
Dynamics of a fractional-order prey-predator reserve biological system incorporating fear effect and mixed functional response PK Santra, GS Mahapatra Brazilian Journal of Physics 54 (1), 14 , 2024 2024 Citations: 4
Chaotic dynamics of the fractional order predator-prey model incorporating Gompertz growth on prey with Ivlev functional response MJ Uddin, PK Santra, SMS Rana, GS Mahapatra Chaos Theory and Applications 6 (3), 192-204 , 2024 2024 Citations: 4
Dynamical behavior and sensitivity analysis of a dengue reinfection model for vertical transmission incorporating multiple control strategies RP Kumar, GS Mahapatra, RD Parshad, PK Santra Commun. Math. Biol. Neurosci. 2023, Article ID 134 , 2023 2023 Citations: 5
COVID-19 Spread Modeling Incorporating Suggestive Optimal Control Strategies under Uncertainty PK Santra, D Pal, GS Mahapatra, H Alrabaiah Advances in Systems Science and Applications 23 (3), 66-90 , 2023 2023
Effect of reliability and memory on fractional inventory model incorporating promotional effort on demand PK Santra, GS Mahapatra, A Kumar RAIRO-Operations Research 57 (4), 1767-1784 , 2023 2023 Citations: 10
MOST CITED SCHOLAR PUBLICATIONS
Mathematical analysis of a COVID-19 epidemic model by using data driven epidemiological parameters of diseases spread in India D Pal, D Ghosh, PK Santra, GS Mahapatra Biophysics 67 (2), 231-244 , 2022 2022 Citations: 64
Bifurcation and Chaos of a Discrete Predator‐Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge PK Santra, GS Mahapatra, GR Phaijoo Mathematical Problems in Engineering 2020 (1), 5309814 , 2020 2020 Citations: 47
Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive RP Kumar, PK Santra, GS Mahapatra Mathematics and computers in simulation 203, 741-766 , 2023 2023 Citations: 41
Optimal control design incorporating vaccination and treatment on six compartment pandemic dynamical system RP Kumar, S Basu, PK Santra, D Ghosh, GS Mahapatra Results in Control and Optimization 7, 100115 , 2022 2022 Citations: 37
A fractional order SITR mathematical model for forecasting of transmission of COVID-19 of India with lockdown effect SS Askar, D Ghosh, PK Santra, AA Elsadany, GS Mahapatra Results in Physics 24, 104067 , 2021 2021 Citations: 34
Dynamical study of discrete-time prey–predator model with constant prey refuge under imprecise biological parameters PK Santra, GS Mahapatra Journal of Biological Systems 28 (03), 681-699 , 2020 2020 Citations: 33
A discrete-time epidemic model for the analysis of transmission of COVID19 based upon data of epidemiological parameters D Ghosh, PK Santra, GS Mahapatra, A Elsonbaty, AA Elsadany The European Physical Journal Special Topics 231 (18), 3461-3470 , 2022 2022 Citations: 31
Bifurcation analysis and chaos control of discrete prey–predator model incorporating novel prey–refuge concept PK Santra, GS Mahapatra, GR Phaijoo Computational and Mathematical Methods 3 (6), e1185 , 2021 2021 Citations: 30
Prey–predator model for optimal harvesting with functional response incorporating prey refuge GS Mahapatra, P Santra International Journal of Biomathematics 9 (01), 1650014 , 2016 2016 Citations: 27
Fractional order inventory system for time-dependent demand influenced by reliability and memory effect of promotional efforts A Kumar, PK Santra, GS Mahapatra Computers & Industrial Engineering 179, 109191 , 2023 2023 Citations: 25
Predator–prey dynamical behavior and stability analysis with square root functional response D Pal, P Santra, GS Mahapatra International Journal of Applied and Computational Mathematics 3 (3), 1833-1845 , 2017 2017 Citations: 25
Preventive control strategy on second wave of Covid-19 pandemic model incorporating lock-down effect S Basu, RP Kumar, PK Santra, GS Mahapatra, AA Elsadany Alexandria Engineering Journal 61 (9), 7265-7276 , 2022 2022 Citations: 24
Dynamical behavior of three species predator–prey system with mutual support between non refuge prey D Pal, P Santra, GS Mahapatra Ecological Genetics and Genomics 3, 1-6 , 2017 2017 Citations: 20
Dynamical analysis of novel COVID‐19 epidemic model with non‐monotonic incidence function R Prem Kumar, S Basu, D Ghosh, PK Santra, GS Mahapatra Journal of Public Affairs 22, e2754 , 2022 2022 Citations: 18
Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete‐Time Prey‐Predator Model GS Mahapatra, PK Santra, E Bonyah Complexity 2021 (1), 6209908 , 2021 2021 Citations: 18
A three-component prey-predator system with interval number D Ghosh, PK Santra, GS Mahapatra Mathematical Modelling and Numerical Simulation with Applications 3 (1), 1-16 , 2023 2023 Citations: 14
Analysis of differential-algebraic prey–predator dynamical model with super predator harvesting on economic perspective P Santra, GS Mahapatra, D Pal International Journal of Dynamics and Control 4 (3), 266-274 , 2016 2016 Citations: 13
Fear effect in discrete prey-predator model incorporating square root functional response PK Santra Jambura Journal of Biomathematics (JJBM) 2 (2), 51-57 , 2021 2021 Citations: 12
Estimasi reproduction number model matematika penyebaran malaria di Sumba Tengah, Indonesia EM Banni, MA Kleden, M Lobo, MZ Ndii Jambura Journal of Biomathematics (JJBM) 2 (1), 13-19 , 2021 2021 Citations: 12
Global stability and sensitivity analysis of parameters of Omicron variant epidemic in diverse susceptible classes incorporating vaccination stages: R. Prem Kumar et al. R Prem Kumar, S Basu, PK Santra, AA Elsadany, A Elsonbaty, ... Soft Computing 28 (6), 4689-4713 , 2024 2024 Citations: 11
