Prabir Sen

Academic professional skilled in developing and delivering engaging lectures and course materials. Focus on fostering collaborative learning environment, conducting research, and publishing findings in peer-reviewed journals. Adept at mentoring students and contributing to departmental initiatives.

• Modelling on Biological phenomena: Modeling biological phenomena involves the use of mathematical, computational, and statistical frameworks to represent and analyze the complex processes underlying life systems. Biological modeling serves as a powerful tool for understanding phenomena such as disease spread, ecological interactions, genetic regulation, and physiological processes. By translating biological questions into mathematical equations or computational algorithms, I can explore scenarios that may be difficult or impossible to test experimentally. Models are continually refined with experimental data to enhance their accuracy and relevance. From studying predator-prey dynamics to tracking pandemics, modeling plays a crucial role in advancing both theoretical knowledge and practical applications in biology.
• Optimal control theory and its application to mathematical biology: Optimal control theory is a mathematical framework used to determine the best possible control strategies for dynamic systems to achieve a desired objective while satisfying given constraints. In mathematical biology, optimal control is extensively applied to model and solve problems in areas such as disease management, ecosystem conservation, and population dynamics. For example, in epidemiology, it is used to design optimal vaccination or treatment strategies that minimize disease spread and associated costs. In ecology, optimal control can guide sustainable harvesting policies or conservation efforts to preserve biodiversity. The theory integrates differential equations to describe biological systems and cost functions to quantify objectives, such as minimizing infection levels, resource consumption, or ecological impact. By combining analytical techniques with numerical methods, optimal control theory provides actionable insights into managing complex biological systems efficiently and effectively.
• · Ecological and Epidemiological Modeling

Ecological and epidemiological modeling is an important interdisciplinary research area that integrates ecological interactions with the spread of infectious diseases in biological populations. It aims to understand how diseases influence the dynamics of species such as prey, predators, hosts, and vectors within an ecosystem. Using mathematical tools such as differential equations, researchers analyze population growth, disease transmission, recovery, predation, competition, and environmental effects simultaneously. These models help explain complex phenomena including species persistence, extinction, oscillatory behavior, and outbreak thresholds. Ecological and epidemiological modeling has wide applications in wildlife conservation, pest management, livestock health, and public health planning, as it provides valuable insights for designing effective control and management strategies.

• · Chaos and Bifurcation Theory

Chaos and bifurcation theory is a significant branch of nonlinear dynamical systems that studies sudden qualitative changes in system behavior and the emergence of complex irregular dynamics as parameters vary. Bifurcation theory explains how small changes in growth rates, transmission coefficients, harvesting levels, or interaction strengths can shift a system from stable equilibrium to periodic oscillations, multiple steady states, or instability. Chaos theory investigates deterministic systems that exhibit highly sensitive dependence on initial conditions, leading to unpredictable long-term behavior despite having fixed governing equations. In ecological and epidemiological models, these concepts are useful for understanding population cycles, disease outbreaks, extinction risks, and abrupt regime shifts. The analysis of chaos and bifurcations helps researchers identify critical thresholds and improve management and control strategies in complex biological systems.

• · Delay Differential Equations

·Delay differential equations are an important class of dynamical systems in which the rate of change of a variable depends not only on its present state but also on its past states. These equations are used to model processes where time delays naturally occur, such as gestation periods, maturation time, incubation delays, immune response lags, and resource regeneration. In ecological and epidemiological modeling, delay differential equations help describe more realistic population growth, predator-prey interactions, and disease transmission dynamics. The inclusion of delays can significantly affect system behavior by generating oscillations, instability, bifurcations, or sustained periodic solutions that may not appear in ordinary differential equation models. Therefore, delay differential equations are valuable tools for understanding memory effects and time-lagged responses in biological and environmental systems.

• Participated in India Biodiversity Meet-2013, Organized by Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata in collaboration with Biomathematical Society of India, India.
• Paper entitled "Role of alternative food in controlling chaotic dynamics in a predator-prey model with disease in predator" presented in National Conference on Mathematical and Theoretical Biology-NCMTB-2014, Department of Mathematics, Jadavpur University, Kolkata, India.
• Participated in the International Conference on Dynamical Systems and Mathematical Biology-ICDSMB-2014, Department of Mathematics, Jadavpur University, Kolkata, India.
• Paper entitled "Defense: An interplay between predator and prey in presence of parasite infection" presented in National Conference on Mathematical and Theoretical Biology-NCMTB-2017, Department of Mathematics, Jadavpur University, Kolkata, India.
• Participated in 5- day National level online workshop on Modelling, Complex Dynamics and Stochastic Differential Equation organised by Calcutta Mathematical Society in 2020, AE-374, Sector I, Salt Lake City, Kolkata - 700064, WB, India.
• Participated in one day National Webinar on Applications of Mathematics on Epidemiology organised by Department Of Mathematics, Vivekananda Satavarshiki Mahavidyalaya, Manikpara, Jhargram, West Bengal-721513 in 2020, India.
• Participated in one day National Conference on Impact of COVID-19 on Indian Economy organised by The Institute of Company Seceretaries of India and Victoria Institution in 2020, Kolkata, India.
• Participated in one day National Webinar on Foundation of ODE with a Case Study organised by City College in 2020, 102/1, Raja Rammohan Sarani, Kolkata-700009, West Bengal, India.
• International virtual Conference on Progress in Mathematics towards Industrial Applications (PMTIA-2022) organised by Department of Mathematics, SRM Institute of Science and Technology, Ramapuram Campus, India.
• Paper entitled "Study of Dynamical Behaviour of an Eco-Epidemiological Model with Adaptive Predation" presented in 5th Regional Science and Technology Congress, 2022-23 organised by Bankura University and Department of Science and Technology and Biotechnology, Government of West Bengal, India.
• Paper entitled "Adaptive Predation Strategy in an Eco-epidemiological Model with Disease in Prey Population" presented in National Conference on Mathematics: Various Aspects in Society in 2023 organised by Department of Mathematics, Jadavpur University, Kolkata, India.
• Paper entitled "Study of Dynamical Behaviors of an Eco-epidemic Model with Allee Effect and Alternative Prey" presented in Indian Biodiversity Meet (IBM-2026), Indian Statistical Institute, Kolkata, India.
• Paper entitled "Multistability and Chaos in the eco-epidemiological system with
  Allee effect" presented in National Conference on Mathematical and Theoretical Biology (NCMTB-2026) in Jadavpur University, Kolkata, India.

• Das, K. P., Bairagi, N., & Sen, P. (2016). Role of alternative food in controlling chaotic dynamics in a predator–prey model with disease in the predator. International Journal of Bifurcation and Chaos, 26(09), 1650147.
• Sen, P., Das, K., & Bairagi, N. (2017). Simultaneous Effects of Prey Defence and Predator Infection on a Predator Prey System. Ann. Bio. Sci, 5(1), 37-46.
• Sen, P., Samanta, S., Khan, M. Y., Mandal, S., & Tiwari, P. K. (2023). A seasonally forced eco-epidemic model with disease in predator and incubation delay. Journal of Biological Systems, 31(03), 921-962.
• Khan, M., Sen, P., & Samanta, S. (2024). Stability and bifurcation analysis of an eco-epidemiological model with prey refuge. Nonlinear Studies, 31(1), 183-209.
• Samanta, S., & Sen, P., Das, K.P. (2024). Multistability and Chaos in the Eco-epidemiological System with Allee Effect. Differential Equations and Dynamical Systems, 1-24.
• Sudip Samanta, Khan Mahammad Yasin, Prabir Sen. (2025). Bifurcation Analysis and Optimal Control in a Predator-Prey-Infection Model with Additional Food. Journal of Innovative Applied Mathematics and Computational Sciences.
• Sudip Samanta, Mahammad Yasin Khan, Riya Kundu, Prabir Sen. (2026). Chaos and bistability in a delayed eco-epidemiological model with fear and Allee effects. International Journal of Biomathematics.
• Prabir Sen, Dr. Sudip Samanta, Mahammad Yasin Khan. (2026). Study of dynamical behaviour of an eco-epidemiological model with Allee effect and alternative prey. Nonlinear Science.

• "Study of dynamical behaviour of an eco-epidemiological model with adaptive predation", Samanta, S., Sen, P. & Khan, M.Y., Brazilian Journal of Physics.

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• Study of dynamical behaviors of a deterministic Eco-epidemic
  model with Beddington-Deangelis functional response and a
  fractional order approach with optimal control strategy.
• Sensitivity and Bifurcation Analysis of SEIR type Dengue Disease Model with Vaccination.
• A stage-structured prey-predator model with Beddington–DeAngelis
  type function response incorporating a prey refuge.
• Aposematism with Beddington-Deanjelis functional response and Shepherd's recruitment function.
• Plant-pest model (Mango-Gall midge system).

Title: Role of alternative food in controlling chaotic dynamics in a predator–prey model with disease in the predator.

• The idea that alternate food stabilises predator-prey interactions is widely acknowledged, though not always. However, parasites have the power to alter the host population's qualitative and quantitative dynamics. In recent times, researchers are showing growing interest in formulating models that integrate both the ecological and epidemiological aspects. In this work We have incorporated alternative food on a predator–prey system with disease in the predator population. We show that the system, in the lack of alternative food, exhibits multiple dynamics viz. stable coexistence, limit cycle oscillations, period-doubling bifurcation and chaos when infection rate is steadily increased. However, our study demonstrates that alternative food may have a greater impact on the community structure and may increase population persistence. The system returns to a regular oscillatory state from a chaotic state through period-halving bifurcations when the predator consumes alternative food in conjunction with its focal prey.

Title: Simultaneous Effects of Prey Defence and Predator Infection on a Predator Prey System.

• Both infection and defensive behaviour play a significant role in population dynamics. Infection can change the quantitative dynamics of its hosts, and defence may assist shield prey from their predator. Here, we have examined a predator-prey model with prey defence, prey cover, and parasitic infections in the predator population. Examining the effects of a predator-prey interaction in the context of prey cover and predator illness is the goal. Bifurcation analysis of all equilibrium points and evidence of local stability are provided in terms of ecological and epidemiological reproduction numbers. It has been demonstrated that infection stabilises a predator-prey system that would otherwise be unstable.
• Title: A seasonally forced eco-epidemic model with disease in predator and incubation delay.

Our current research is based on the investigation of an eco-epidemiological model that solely includes illness in predators. Predators, both healthy and diseased, are thought to consume prey and breed; however, the offsprings are expected to be vulnerable. To achieve a more realistic and explicit outcome of the existing phenomena correlated with our model system, we consider that the process of disease transmission is mediated by some time lag and the intensity of disease prevalence is seasonally forced. Our simulation results show that the disease dies out for lower intensity of disease prevalence or higher rate of consumption of prey by susceptible predator. The system undergoes subcritical/supercritical Hopf bifurcation due to changes in the parameters representing the intensity of disease prevalence, consumption rate of prey by susceptible/infected predator. The system exhibits two types of bistabilities: the first one between stable coexistence and oscillating coexistence, and the second one between two oscillatory coexistence cycles. Moreover, we see that with gradual increase in the incubation delay, the system shows transitions from stable focus to limit cycle oscillations to period doubling oscillations to chaotic dynamics. Chaotic dynamics is also observed for the periodic changes in the intensity of disease prevalence if it takes much time for the pathogens to develop sufficiently inside the body of the susceptible predator population.

• Title: Stability and bifurcation analysis of an eco-epidemiological model with prey refuge.

In this paper, we propose and analyse a predator-prey model with disease in prey. We assume that a portion of healthy prey takes refuge to avoid predation. We find the biologically feasible equilibrium points and their stability criteria by using linearization technique. We also perform Hopf bifurcation analysis around the coexisting equilibrium point. We carry out extensive numerical simulation to validate our theoretical results and also explore rich dynamics which cannot be attained analytically. We draw some one and two parameter bifurcation diagrams which demonstrate rich dynamics like, Hopf bifurcation, chaos, bistability, etc. We observe that invasion of disease in prey can produce chaos through period-doubling bifurcation, whereas refuge can control chaos via period-halving bifurcation. We also observe that refuge can control disease prevalence in the prey population.

• Title: Multistability and Chaos in the Eco-epidemiological System with Allee Effect.

In this research work, the Rosenzweig-MacArthur model comprises with the predator population afflicted by illness has been studied. We may investigate the effects of Allee effects further by looking at populations of predators and prey with a weak Allee effect and prey with a strong Allee effect. We carry out analytical analyses of equilibrium, stability, and Hopf bifurcation. We have also investigated, via numerical simulations, chaotic dynamics for a progressive rise in the force of infection. We see that a strong Allee effect can keep the system from going into chaos, but that once the strong Allee parameter reaches a certain value, the prey population goes extinct and as a result, also the predator population extincts too. However, the weak Allee effect also has a important impact on population dynamics and has the potential to increase the number of predators. To investigate the complex dynamics of the system, we have created a number of bifurcation diagrams with one and two parameters. We also note that at appropriate parameter values, the system may display tri-stability and bi-stability.

• Title: Bifurcation Analysis and Optimal Control in a Predator-Prey-Infection Model with Additional Food.

We propose and analyze a three-dimensional eco-epidemiological model involving susceptible prey, infected prey, and predators, where the predators are supplemented with an externally supplied constant quantity of additional food. The model incorporates nonlinear disease transmission and predator feeding saturation through a generalized Holling type II functional response. We investigate the system’s dynamics analytically and numerically by studying the existence and stability of equilibria, as well as bifurcations including Hopf, transcritical, and saddle-node bifurcations. One and two parameter bifurcation analyses reveal rich dynamics such as limit cycles, period-doubling, and chaotic oscillations. Our findings indicate that disease transmission can destabilize the system, while the inclusion of additional food enhances stability and can suppress chaos. Furthermore, we extend the model by introducing a time-dependent optimal control variable representing additional food supply, and derive an optimal strategy using Pontryagin’s Maximum Principle. Numerical simulations show that the optimal control effectively reduces disease prevalence and stabilizes the population dynamics. This study highlights the potential of ecological interventions, such as strategic food supplementation, in regulating complex eco-epidemiological systems.

• Title: Chaos and bi-stability in a delayed eco-epidemiological model with fear and Allee effects.

Eco-epidemiological systems, in which infectious diseases interact with ecological processes such as predation and competition, exhibit rich and often counterintuitive dynamics. In predator–prey systems where the prey population is subject to disease, additional ecological mechanisms such as the Allee effect and non-consumptive fear responses can critically influence stability, persistence, and extinction outcomes. Furthermore, biological processes like predator gestation introduce time delays that can fundamentally alter system trajectories. In this study, we develop and analyze a nonlinear predator–prey–disease model incorporating (i) a strong Allee effect in the prey population, (ii) fear-mediated reductions in prey growth rates, and (iii) an explicit gestation delay in predator reproduction. Analytical investigations are conducted to determine the existence and stability conditions of equilibria, extinction thresholds, and bifurcation structures. The delay is treated as a bifurcation parameter to assess its influence on the stability of the coexistence equilibrium and the onset of oscillatory dynamics. Numerical simulations further reveal delay-induced destabilization, bistability, and shifts in the basins of attraction. The results highlight how the combined effects of ecological constraints, behavioral adaptations, and epidemiological factors shape the qualitative dynamics of eco-epidemiological systems, offering new insights into population persistence and control strategies.

• Title: Study of dynamical behaviour of an eco-epidemiological model with Allee effect and alternative prey.

In this research work, an eco-epidemiological model comprises with disease in prey population and strong Allee effect also in prey population has been considered. In this work, we have also considered alternative prey as living prey population. We carry out the analytical analysis of equilibria and stability. We also investigated via numerical analysis, chaotic dynamics of the system for progressive increment of disease in prey population. We see that if strong Allee effect parameter crosses the certain value, the system settles down to stability. However, the alternative prey population has an important impact on population dynamics making the system stable first and then gradually disease free. To understand the complex dynamics of the system, we have also investigated different one parametric bifurcation and two parametric bifurcation. We have also noted that, for appropriate parameter values, the system shows different bi-stability in different regions.

• Title: Study of dynamical behaviour of an eco-epidemilogical model with adaptive predation

In this work we have analyzed an eco-epidemic model with adaptive predation strategy in predator population. We have drawn average fitness function of foraging strategy and analyzed the stability of the system for two different cases. The subsystem shows chaotic dynamics for increasing infection ratethrough period doubling bifurcation. And also shows bi-stability between interior equilibrium and stable limit cycle. To show the rich dynamics of the system we have drawn two parametric bifurcation in different parametric space.

• Study of dynamical behaviors of a deterministic Eco-epidemic
  model with Beddington-Deangelis functional response and a
  fractional order approach with optimal control strategy.

This study focuses on the dynamical behavior of a deterministic eco-epidemic model incorporating the Beddington-DeAngelis functional response and a fractional-order framework with an optimal control strategy. The model describes the interactions between prey and predator populations in the presence of infectious disease, where the Beddington-DeAngelis functional response accounts for predator interference and more realistic predation behavior. The use of fractional-order derivatives introduces memory and hereditary effects, making the system better suited to represent real biological processes. Qualitative analysis such as positivity, boundedness, equilibrium existence, local and global stability, bifurcation, and persistence can be investigated to understand the long-term dynamics of the system. Furthermore, optimal control techniques are applied to determine effective strategies such as treatment, vaccination, harvesting, or culling while minimizing economic and ecological costs. This approach provides deeper insight into disease management and ecosystem sustainability.

• Title: Sensitivity and Bifurcation Analysis of SEIR type Dengue Disease Model with Vaccination

This study deals with the sensitivity and bifurcation analysis of an SEIR-type dengue disease model incorporating vaccination as a control measure. The population is divided into susceptible, exposed, infected, and recovered classes to describe the transmission dynamics of dengue fever. Vaccination is included to reduce susceptibility and limit the spread of infection within the community. Sensitivity analysis is performed to identify the most influential parameters affecting the basic reproduction number and disease prevalence, such as transmission rate, recovery rate, mosquito biting rate, and vaccine efficacy. Bifurcation analysis is used to examine qualitative changes in system behavior, including the possibility of backward or forward bifurcation, multiple endemic equilibria, and threshold dynamics near the critical reproduction number. This investigation provides important insights for designing efficient vaccination policies and public health strategies for dengue prevention and control.

• Title: A stage-structured prey-predator model with Beddington–DeAngelis type function response incorporating a prey refuge.

This study considers a stage-structured prey-predator model with a Beddington–DeAngelis type functional response incorporating prey refuge. The prey population is divided into different life stages, such as juvenile and mature classes, to represent realistic growth and maturation processes. The Beddington–DeAngelis functional response is used to describe predation more accurately by including mutual interference among predators during hunting. A prey refuge is introduced to represent a proportion of prey protected from predation due to hiding places or environmental shelter. The model is used to investigate important dynamical properties such as positivity, boundedness, equilibrium existence, local and global stability, persistence, and bifurcation behavior. The inclusion of stage structure and refuge mechanisms provides deeper insight into species coexistence, predator survival, and ecological balance in natural ecosystems.

• Title: Aposematism with Beddington-Deanjelis functional response and Shepherd’s recruitment function.

This study examines an ecological model of aposematism incorporating the Beddington–DeAngelis functional response and Shepherd’s recruitment function. Aposematism refers to the use of warning coloration or signals by prey species to reduce predation by indicating toxicity or unpalatability. The Beddington–DeAngelis functional response is employed to represent realistic predator-prey interactions by accounting for predator interference during the searching and handling process. Shepherd’s recruitment function is used to model density-dependent population recruitment, allowing flexible growth behavior under low and high population densities. The combined model can be analyzed to investigate key dynamical features such as equilibrium existence, stability, persistence, oscillatory dynamics, and bifurcation phenomena. This framework helps explain how warning signals, predator behavior, and population regulation jointly influence species survival and long-term ecological balance.

• Title: Plant-pest model (Mango-Gall midge system).

This study focuses on a plant-pest interaction model based on the Mango–Gall midge system, where mango plants serve as the host and gall midges act as destructive pests. Gall midges damage leaves, flowers, and developing tissues, reducing plant growth, fruit yield, and overall productivity. The mathematical model describes the population dynamics between mango plants and pest species by incorporating factors such as plant growth, pest infestation, reproduction, natural mortality, and possible control measures. Analysis of the system may include equilibrium points, stability behavior, persistence, threshold conditions, and bifurcation dynamics. The model can also be extended to include biological control, pesticide application, seasonal effects, or delay factors. Such studies are useful for understanding pest outbreaks and developing effective management strategies for sustainable mango cultivation.

• Badminton & Table tennis.
• Meditation & Chanting.