Kalyan Manna

Scopus Publications

Spatiotemporal patterns of social protests: Reaction–diffusion approach
Andrew Morozov, Kalyan Manna, Malay Banerjee, Sergei Petrovskii
Chaos Solitons and Fractals, 2026
Exploring the structural sensitivity in some spatially-explicit models of ecological dynamics
Kalyan Manna, Malay Banerjee, Sergei Petrovskii
Chaos Solitons and Fractals, 2026
Mathematical models are frequently used to infer predictions about population dynamics in real ecosystems. However, parametrization of intra- and interspecific interactions is usually approximate, as the amount and quality of ecological information is never sufficient to make a ‘precise’ decision about the mathematical function(s) to use. The question therefore arises as to how sensitive the model properties can be with regard to the choice of the function - the problem known as “structural sensitivity”. In this article, we explore the structural sensitivity of a predator–prey model with additive Allee effect in prey growth and density-dependent death rate for predator. We test the sensitivity of both temporal (non-spatial) and spatiotemporal (spatially-explicit) models using three qualitatively similar but numerically different parametrizations of the predator functional response, such as Holling type II (fraction-linear), Ivlev (exponential) and hyperbolic (trigonometric) functions. Using an array of the analytical and numerical tools, we show that both the temporal and spatiotemporal dynamics can be qualitatively different for the three chosen parametrizations. Also, our study clearly reveals that any hierarchical ranking of these parametrizations according to their destabilizing potential is not possible.
Biological models with nonlocal terms: Future scopes of research: Comment on “Nonlocal models in biology and life sciences: Sources, developments, and applications” by S. Pal & R. Melnick
Malay Banerjee, Kalyan Manna, Indrajyoti Gaine
Physics of Life Reviews, 2026
EFFECTS OF SPATIOTEMPORAL, TEMPORAL AND SPATIAL NONLOCAL PREY COMPETITIONS ON POPULATION DISTRIBUTIONS FOR A PREY-PREDATOR SYSTEM WITH GENERALIST PREDATION
Kalyan Manna, Swadesh Pal, Malay Banerjee
Discrete and Continuous Dynamical Systems Series B, 2026
Conventional wisdom suggests that a prey-predator system with a generalist predator exhibits more stable dynamics than with a specialist predator. However, recent developments show that the presence of a generalist predator can lead to comparatively complex dynamics, including bistability, tristability, and several local as well as global bifurcations. In this paper, we study the dynamics of both local and nonlocal models of prey-predator interactions with generalist-type predation. Nonlocal intra-specific prey competition is assumed to be spatiotemporal, purely temporal, or purely spatial in nature. Also, we primarily aim to understand the resulting system dynamics under conditions of subpar and limited substitute food options available to the generalist predator. We first ensure that the local model is well-posed, and then provide the conditions for the existence and non-existence of spatially heterogeneous steady state solutions by using the maximum principle, Poincaré inequality and Leray-Schauder degree theory. Further, we derive the conditions for Turing instability in both the local and nonlocal models by using the linear analysis. We then illustrate a wide class of stationary and dynamic patterns obtained through numerical simulations for all the considered models, where the choice of the parametric domain is partially guided by the analytical results. This study reveals that the nonlocal model with purely spatial kernel admits spatial-Hopf bifurcation which gives rise to population oscillations around a 'ghost attractor', whereas this phenomenon does not occur in the other models.
On the structural sensitivity of some diffusion–reaction models of population dynamics
Kalyan Manna, Malay Banerjee, Sergei Petrovskii
Physica D Nonlinear Phenomena, 2024
In mathematical ecology, it is often assumed that properties of a mathematical model are robust to specific parameterization of functional responses, in particular preserving the bifurcation structure of the system, as long as different functions are qualitatively similar. This intuitive assumption has been challenged recently (Fussmann & Blasius, Community response to enrichment is highly sensitive to model structure, Biology Letters 1:9-12, 2005). Having considered the prey-predator system as a paradigm of nonlinear population dynamics, it has been shown that in fact both the bifurcation structure and the structure of the phase space can be rather different even when the component functions are apparently close to each other. However, these observations have so far been largely limited to nonspatial systems described by ODEs. In this paper, our main motivating interest is to investigate whether such structural sensitivity occurs in spatially explicit models of population dynamics, in particular those that are described by PDEs. We consider a prey-predator model described by a system of two nonlinear reaction–diffusion-advection equations where the predation term is parameterized by three different yet numerically close functions. Using some analytical tools along with numerical simulations, we show that the properties of spatiotemporal dynamics are rather different between the three cases, so that patterns observed for one parameterization may not occur for the other two ones.
Dynamics of a prey–predator model with reproductive Allee effect for prey and generalist predator
Kalyan Manna, Malay Banerjee
Nonlinear Dynamics, 2024
A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study
Kalyan Manna, Khalid Hattaf
Mathematical Methods in the Applied Sciences, 2022
In this paper, we formulate a generalized hepatitis B virus (HBV) infection model with two modes of infection transmission and adaptive immunity and investigate its dynamical properties. Both the virus‐to‐cell and cell‐to‐cell infection transmissions are modeled by general functions which satisfy some biologically motivated assumptions. Furthermore, the model incorporates three distributed time delays for the production of active infected hepatocytes, mature capsids, and virions. The well‐posedness of the proposed model is established by showing the non‐negativity and boundedness of solutions. Five equilibria of the model are identified in terms of five threshold parameters R0,R1,R2,R3$$ {R}_0,{R}_1,{R}_2,{R}_3 $$ , and R4$$ {R}_4 $$ . Further, the global stability analysis of each equilibrium under certain conditions is carried out by employing suitable Lyapunov function and LaSalle's invariance principle. Finally, we present an example with numerical simulations to illustrate the applicability of our study. Nonetheless, the results obtained in this study are valid for a wide class of HBV infection models.
Spatiotemporal pattern formation in a prey predator model with generalist predator
Kalyan Manna, Malay Banerjee
Mathematical Modelling of Natural Phenomena, 2022
Generalist predators exploit multiple food sources and it is economical for them to reduce predation pressure on a particular prey species when their density level becomes comparatively less. As a result, a prey-predator system tends to become more stable in the presence of a generalist predator. In this article, we investigate the roles of both the diffusion and nonlocal prey consumption in shaping the population distributions for interacting generalist predator and its focal prey species. In this regard, we first derive the conditions associated with Turing instability through linear analysis. Then, we perform a weakly nonlinear analysis and derive a cubic Stuart-Landau equation governing amplitude of the resulting patterns near Turing bifurcation boundary. Further, we present a wide variety of numerical simulations to corroborate our analytical findings as well as to illustrate some other complex spatiotemporal dynamics. Interestingly, our study reveals the existence of traveling wave solutions connecting two spatially homogeneous coexistence steady states in Turing domain under the influence of temporal bistability phenomenon. Also, our investigation shows that nonlocal prey consumption acts as a stabilizing force for the system dynamics.
Pattern Formation in a Three-Species Cyclic Competition Model
Kalyan Manna, Vitaly Volpert, Malay Banerjee
Bulletin of Mathematical Biology, 2021
Analytical and numerical detection of traveling wave and wave-train solutions in a prey–predator model with weak Allee effect
Kalyan Manna, Swadesh Pal, Malay Banerjee
Nonlinear Dynamics, 2020
Modeling the dynamics of hepatitis B virus infection in presence of capsids and immunity
Khalid Hattaf, Kalyan Manna
Studies in Systems Decision and Control, 2020
Dynamics of a diffusive two-prey-one-predator model with nonlocal intra-specific competition for both the prey species
Kalyan Manna, Vitaly Volpert, Malay Banerjee
Mathematics, 2020
Spatiotemporal dynamics of a generalized hbv infection model with capsids and adaptive immunity
Kalyan Manna, Khalid Hattaf
International Journal of Applied and Computational Mathematics, 2019
Stability of Hopf-bifurcating limit cycles in a diffusion-driven prey-predator system with Allee effect and time delay
Kalyan Manna,, Malay Banerjee
Mathematical Biosciences and Engineering, 2019
Stationary, non-stationary and invasive patterns for a prey-predator system with additive Allee effect in prey growth
Kalyan Manna, Malay Banerjee
Ecological Complexity, 2018
Dynamics of a Delayed Diffusive HBV Infection Model with Capsids and CTL Immune Response
Kalyan Manna
International Journal of Applied and Computational Mathematics, 2018
Combination therapy of pegylated interferon and lamivudine and optimal controls for chronic hepatitis B infection
Kalyan Manna, Siddhartha P. Chakrabarty
International Journal of Dynamics and Control, 2018
A non-standard finite difference scheme for a diffusive HBV infection model with capsids and time delay
Kalyan Manna
Journal of Difference Equations and Applications, 2017
Global Properties of a HBV Infection Model with HBV DNA-Containing Capsids and CTL Immune Response
Kalyan Manna
International Journal of Applied and Computational Mathematics, 2017
Dynamics of a diffusion-driven HBV infection model with capsids and time delay
Kalyan Manna
International Journal of Biomathematics, 2017
Global stability of one and two discrete delay models for chronic hepatitis B infection with HBV DNA-containing capsids
Kalyan Manna, Siddhartha P. Chakrabarty
Computational and Applied Mathematics, 2017
Dynamics and analysis of a model for chronic hepatitis B infection
Kalyan Manna, Siddhartha P. Chakrabarty
Journal of Interdisciplinary Mathematics, 2017
Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids
Kalyan Manna, Siddhartha P. Chakrabarty
Journal of Difference Equations and Applications, 2015
Chronic hepatitis B infection and HBV DNA-containing capsids: Modeling and analysis
Kalyan Manna, Siddhartha P. Chakrabarty
Communications in Nonlinear Science and Numerical Simulation, 2015

RECENT SCHOLAR PUBLICATIONS

Spatiotemporal patterns of social protests: Reaction-diffusion approach
A Morozov, K Manna, M Banerjee, S Petrovskii
Chaos, Solitons & Fractals 208 (2), 118184 , 2026
2026
Exploring the structural sensitivity in some spatially-explicit models of ecological dynamics
K Manna, M Banerjee, S Petrovskii
Chaos, Solitons & Fractals 204, 117759 , 2026
2026
Citations: 1
Biological models with nonlocal terms: Future scopes of research: Comment on “Nonlocal models in biology and life sciences: Sources, developments, and applications” by S. Pal …
M Banerjee, K Manna, I Gaine
Physics of Life Reviews 56, 29-32 , 2026
2026
Effects of spatiotemporal, temporal and spatial nonlocal prey competitions on population distributions for a prey-predator system with generalist predation
K Manna, S Pal, M Banerjee
Discrete and Continuous Dynamical Systems- Series B 31 (1), 166-197 , 2026
2026
Dynamics of a within-host HIV infection model with adaptive immunity
S Samaddar, K Manna, M Banerjee
Mathematics for Industry 38, 29-52 , 2024
2024
Citations: 1
On the structural sensitivity of some diffusion-reaction models of population dynamics
K Manna, M Banerjee, S Petrovskii
Physica D: Nonlinear Phenomena 467, 134220 , 2024
2024
Citations: 12
Dynamics of a prey–predator model with reproductive Allee effect for prey and generalist predator
K Manna, M Banerjee
Nonlinear Dynamics 112 (9), 7727-7748 , 2024
2024
Citations: 22
A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study
K Manna, K Hattaf
Mathematical Methods in the Applied Sciences 45 (17), 11614-11634 , 2022
2022
Citations: 10
Spatiotemporal pattern formation in a prey-predator model with generalist predator
K Manna, M Banerjee
Mathematical Modelling of Natural Phenomena 17, 6 , 2022
2022
Citations: 22
Pattern formation in a three-species cyclic competition model
K Manna, V Volpert, M Banerjee
Bulletin of Mathematical Biology 83 (5), 52 , 2021
2021
Citations: 32
Analytical and numerical detection of traveling wave and wave-train solutions in a prey-predator model with weak Allee effect
K Manna, S Pal, M Banerjee
Nonlinear Dynamics 100 (3), 2989-3006 , 2020
2020
Citations: 9
Dynamics of a diffusive two-prey-one-predator model with nonlocal intra-specific competition for both the prey species
K Manna, V Volpert, M Banerjee
Mathematics 8 (1), 101 , 2020
2020
Citations: 32
Modeling the dynamics of hepatitis B virus infection in presence of capsids and immunity
K Hattaf, K Manna
Studies in Systems, Decision and Control 302, 269-294 , 2020
2020
Citations: 12
Spatiotemporal dynamics of a generalized HBV infection model with capsids and adaptive immunity
K Manna, K Hattaf
International Journal of Applied and Computational Mathematics 5 (3), 65 , 2019
2019
Citations: 24
Stability of Hopf-bifurcating limit cycles in a diffusion-driven prey-predator system with Allee effect and time delay
K Manna, M Banerjee
Mathematical Biosciences and Engineering 16 (4), 2411-2446 , 2019
2019
Citations: 19
Stationary, non-stationary and invasive patterns for a prey-predator system with additive Allee effect in prey growth
K Manna, M Banerjee
Ecological Complexity 36, 206-217 , 2018
2018
Citations: 34
Dynamics of a delayed diffusive HBV infection model with capsids and CTL immune response
K Manna
International Journal of Applied and Computational Mathematics 4 (5), 116 , 2018
2018
Citations: 18
Combination therapy of pegylated interferon and lamivudine and optimal controls for chronic hepatitis B infection
K Manna, SP Chakrabarty
International Journal of Dynamics and Control 6 (1), 354-368 , 2018
2018
Citations: 14
A non-standard finite difference scheme for a diffusive HBV infection model with capsids and time delay
K Manna
Journal of Difference Equations and Applications 23 (11), 1901-1911 , 2017
2017
Citations: 20
Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response
K Manna
International Journal of Applied and Computational Mathematics 3 (3), 2323-2338 , 2017
2017
Citations: 39

MOST CITED SCHOLAR PUBLICATIONS

Chronic hepatitis B infection and HBV DNA-containing capsids: Modeling and analysis
K Manna, SP Chakrabarty
Communications in Nonlinear Science and Numerical Simulation 22 (1-3), 383-395 , 2015
2015
Citations: 90
Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids
K Manna, SP Chakrabarty
Journal of Difference Equations and Applications 21 (10), 918-933 , 2015
2015
Citations: 61
Global stability of one and two discrete delay models for chronic hepatitis B infection with HBV DNA-containing capsids
K Manna, SP Chakrabarty
Computational and Applied Mathematics 36 (1), 525-536 , 2017
2017
Citations: 58
Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response
K Manna
International Journal of Applied and Computational Mathematics 3 (3), 2323-2338 , 2017
2017
Citations: 39
Stationary, non-stationary and invasive patterns for a prey-predator system with additive Allee effect in prey growth
K Manna, M Banerjee
Ecological Complexity 36, 206-217 , 2018
2018
Citations: 34
Pattern formation in a three-species cyclic competition model
K Manna, V Volpert, M Banerjee
Bulletin of Mathematical Biology 83 (5), 52 , 2021
2021
Citations: 32
Dynamics of a diffusive two-prey-one-predator model with nonlocal intra-specific competition for both the prey species
K Manna, V Volpert, M Banerjee
Mathematics 8 (1), 101 , 2020
2020
Citations: 32
Spatiotemporal dynamics of a generalized HBV infection model with capsids and adaptive immunity
K Manna, K Hattaf
International Journal of Applied and Computational Mathematics 5 (3), 65 , 2019
2019
Citations: 24
Dynamics of a prey–predator model with reproductive Allee effect for prey and generalist predator
K Manna, M Banerjee
Nonlinear Dynamics 112 (9), 7727-7748 , 2024
2024
Citations: 22
Spatiotemporal pattern formation in a prey-predator model with generalist predator
K Manna, M Banerjee
Mathematical Modelling of Natural Phenomena 17, 6 , 2022
2022
Citations: 22
Dynamics of a diffusion-driven HBV infection model with capsids and time delay
K Manna
International Journal of Biomathematics 10 (5), 1750062 (18 pages) , 2017
2017
Citations: 21
A non-standard finite difference scheme for a diffusive HBV infection model with capsids and time delay
K Manna
Journal of Difference Equations and Applications 23 (11), 1901-1911 , 2017
2017
Citations: 20
Stability of Hopf-bifurcating limit cycles in a diffusion-driven prey-predator system with Allee effect and time delay
K Manna, M Banerjee
Mathematical Biosciences and Engineering 16 (4), 2411-2446 , 2019
2019
Citations: 19
Dynamics of a delayed diffusive HBV infection model with capsids and CTL immune response
K Manna
International Journal of Applied and Computational Mathematics 4 (5), 116 , 2018
2018
Citations: 18
Combination therapy of pegylated interferon and lamivudine and optimal controls for chronic hepatitis B infection
K Manna, SP Chakrabarty
International Journal of Dynamics and Control 6 (1), 354-368 , 2018
2018
Citations: 14
On the structural sensitivity of some diffusion-reaction models of population dynamics
K Manna, M Banerjee, S Petrovskii
Physica D: Nonlinear Phenomena 467, 134220 , 2024
2024
Citations: 12
Modeling the dynamics of hepatitis B virus infection in presence of capsids and immunity
K Hattaf, K Manna
Studies in Systems, Decision and Control 302, 269-294 , 2020
2020
Citations: 12
A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study
K Manna, K Hattaf
Mathematical Methods in the Applied Sciences 45 (17), 11614-11634 , 2022
2022
Citations: 10
Analytical and numerical detection of traveling wave and wave-train solutions in a prey-predator model with weak Allee effect
K Manna, S Pal, M Banerjee
Nonlinear Dynamics 100 (3), 2989-3006 , 2020
2020
Citations: 9
Dynamics and analysis of a model for chronic hepatitis B infection
K Manna, SP Chakrabarty
Journal of Interdisciplinary Mathematics 20 (2), 339-355 , 2017
2017
Citations: 4

Kalyan Manna

EDUCATION

RESEARCH INTERESTS

Scopus Publications

RECENT SCHOLAR PUBLICATIONS

MOST CITED SCHOLAR PUBLICATIONS