arXiv subjects

Malay Banerjee

Publications and source records attributed to Malay Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

Modeling of Pneumococcal and Respiratory Syncytial Virus Pneumonia: An Epidemiological Review, with Statistical Inference

Infectious diseases continue to pose significant public health challenges worldwide, requiring effective prevention and control strategies to mitigate their negative impact. Infectious diseases can be broadly classified into two groups: vaccine-preventable diseases (e.g., measles, polio, influenza, hepatitis B, pneumonia) and vaccine-non-preventable diseases (e.g., HIV/AIDS). Vaccine-preventable disease models are one of the essential tools for understanding infectious disease dynamics, evaluating intervention strategies, and guiding public health policies. In this review article, we explore the recent advancements in modeling two particular vaccine-preventable infectious diseases. Here, we consider both deterministic and stochastic models to comprehensively capture the complexity of disease transmission, vaccine efficacy, and population-level immunity. We highlight the application of these models to the infectious diseases, namely, bacterial and viral pneumonia caused by the bacteria Streptococcus pneumoniae (S. pneumoniae) and the respiratory syncytial virus (RSV). Pneumonia carry a substantial global burden, where modeling has played a crucial role in assessing vaccine impacts and optimizing immunization strategies to minimize the disease burden. By synthesizing recent methodologies and findings, this review provides valuable insights for future research and policy decisions aimed at improving vaccine-preventable disease control for pneumonia caused by S. pneumoniae and RSV.

q-bio.PE↗

arXiv2025

Effect of Vaccine Dose Intervals: Considering Immunity Levels, Vaccine Efficacy, and Strain Variants for Disease Control Strategy

In this study, we present an immuno-epidemic model to understand mitigation options during an epidemic break. The model incorporates comorbidity and multiple-vaccine doses through a system of coupled integro-differential equations to analyze the epidemic rate and intensity from a knowledge of the basic reproduction number and time-distributed rate functions. Our modeling results show that the interval between vaccine doses is a key control parameter that can be tuned to significantly influence disease spread. We show that multiple doses induce a hysteresis effect in immunity levels that offers a better mitigation alternative compared to frequent vaccination which is less cost-effective while being more intrusive. Optimal dosing intervals, emphasizing the cost-effectiveness of each vaccination effort, and determined by various factors such as the level of immunity and efficacy of vaccines against different strains, appear to be crucial in disease management. The model is sufficiently generic that can be extended to accommodate specific disease forms.

q-bio.PE↗

arXiv2025

Spatio-temporal pattern formation under varying functional response parametrizations

Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data, especially for complex ecological interactions creates uncertainty in model predictions, often requiring adjustments to the mathematical formulation of these interactions. Modifying the mathematical representation of components responsible for complex behaviors, such as predation, can further contribute to this uncertainty, a phenomenon known as structural sensitivity. Structural sensitivity has been explored primarily in non-spatial systems governed by ordinary differential equations (ODEs), and in a limited number of simple, spatially extended systems modeled by nonhomogeneous parabolic partial differential equations (PDEs), where self-diffusion alone cannot produce spatial patterns. In this study, we broaden the scope of structural sensitivity analysis to include spatio-temporal ecological systems in which spatial patterns can emerge due to diffusive instability. Through a combination of analytical techniques and supporting numerical simulations, we show that pattern formation can be highly sensitive to how the system and its associated ecological interactions are mathematically parameterized. In fact, some patterns observed in one version of the model may completely disappear in another with a different parameterization, even though the underlying properties remain unchanged.

nlin.PS↗

arXiv2025

Mathematical Modeling, Analysis and Simulation Utilizing Machine Learning Tools for Assessing the Impact of Climate Lobbying

Climate policy and legislation has a significant influence on both domestic and global responses to the pressing environmental challenges of our time. The effectiveness of such climate legislation is closely tied to the complex dynamics among elected officials, a dynamic significantly shaped by the relentless efforts of lobbying. This project aims to develop a novel compartmental model to forecast the trajectory of climate legislation within the United States. By understanding the dynamics surrounding floor votes, the ramifications of lobbying, and the flow of campaign donations within the chambers of the U.S. Congress, we aim to validate our model through a comprehensive case study of the American Clean Energy and Security Act (ACESA). Our model adeptly captures the nonlinear dynamics among diverse legislative factions, including centrists, ardent supporters, and vocal opponents of the bill, culminating in a rich dynamics of final voting outcomes. We conduct a stability analysis of the model, estimating parameters from public lobbying records and a robust body of existing literature. The numerical verification against the pivotal 2009 ACESA vote, alongside contemporary research, underscores the models promising potential as a tool to understand the dynamics of climate lobbying. We also analyse the pathways of the model that aims to guide future legislative endeavors in the pursuit of effective climate action.

physics.soc-ph↗

arXiv2024

Estimation of time-varying recovery and death rates from epidemiological data: A new approach

The time-to-recovery or time-to-death for various infectious diseases can vary significantly among individuals, influenced by several factors such as demographic differences, immune strength, medical history, age, pre-existing conditions, and infection severity. To capture these variations, time-since-infection dependent recovery and death rates offer a detailed description of the epidemic. However, obtaining individual-level data to estimate these rates is challenging, while aggregate epidemiological data (such as the number of new infections, number of active cases, number of new recoveries, and number of new deaths) are more readily available. In this article, a new methodology is proposed to estimate time-since-infection dependent recovery and death rates using easily available data sources, accommodating irregular data collection timings reflective of real-world reporting practices. The Nadaraya-Watson estimator is utilized to derive the number of new infections. This model improves the accuracy of epidemic progression descriptions and provides clear insights into recovery and death distributions. The proposed methodology is validated using COVID-19 data and its general applicability is demonstrated by applying it to some other diseases like measles and typhoid.

stat.AP↗

arXiv2024

An age-distributed immuno-epidemiological model with information-based vaccination decision

A new age-distributed immuno-epidemiological model with information-based vaccine uptake suggested in this work represents a system of integro-differential equations for the numbers of susceptible individuals, infected individuals, vaccinated individuals and recovered individuals. This model describes the influence of vaccination decision on epidemic progression in different age groups. We prove the existence and uniqueness of a positive solution using the fixed point theory. In a particular case of age-independent model, we determine the final size of epidemic, that is, the limiting number of susceptible individuals at asymptotically large time. Numerical simulations show that the information-based vaccine acceptance can significantly influence the epidemic progression. Though the initial stage of epidemic progression is the same for all memory kernels, as the epidemic progresses and more information about the disease becomes available, further epidemic progression strongly depends on the memory effect. Short-range memory kernel appears to be more effective in restraining the epidemic outbreaks because it allows for more responsive and adaptive vaccination decisions based on the most recent information about the disease.

q-bio.PE↗

arXiv2023

The Role of Soil Surface in a Sustainable Semiarid Ecosystem

Patterns in a semiarid ecosystem are important because they directly and indirectly affect ecological processes, biodiversity, and ecosystem resilience. Understanding the causes and effects of these patterns is critical for long-term land surface management and conservation efforts in semiarid regions, which are especially sensitive to climate change and human-caused disturbances. It is known that there is a regular connection between the vegetation and the living species in a habitat since some animals evolved to live in a semiarid ecosystem and rely on plants for food. In this work, we have constructed a coupled mathematical model to connect the water resource, vegetation and living organisms and have investigated how the soil surface affects the resulting patterns for the long term. This study contributes to a better understanding of ecological patterns and processes in semiarid environments by shedding light on the complex interaction mechanisms that depend on the structure of semiarid ecosystems. The findings provide further critical insight into the influence of efforts for improving ecosystem resilience and adjusting to the challenges posed by climate change and human activities.

q-bio.PE↗

arXiv2023

A two-timescale model of plankton-oxygen dynamics predicts formation of Oxygen Minimum Zones and global anoxia

Decline of the dissolved oxygen in the ocean is a growing concern, as it may eventually lead to global anoxia, an elevated mortality of marine fauna and even a mass extinction. Deoxygenation of the ocean often results in the formation of Oxygen Minimum Zones (OMZ): large domains where the abundance of oxygen is much lower than that in the surrounding ocean environment. Factors and processes resulting in the OMZ formation remain controversial. We consider a conceptual model of coupled plankton-oxygen dynamics that, apart from the plankton growth and the oxygen production by phytoplankton, also accounts for the difference in the timescales for phyto and zooplankton (making it a "slow-fast system") and for the implicit effect of upper trophic levels. The model is investigated using a combination of analytical techniques and numerical simulations. We show that the system does not allow for persistent relaxation oscillations; instead, the blowup of the canard cycle results in plankton extinction and oxygen depletion. For the spatially explicit model, an initial non-uniform perturbation can lead to the formation of an OMZ, which then grows in size and spreads over space. For a sufficiently large timescale separation, the spread of the OMZ can result in global anoxia.

math.DS↗

arXiv2023

Normal form for singular Bautin bifurcation in a slow-fast system with Holling type III functional response

Over the last few decades, complex oscillations of slow-fast systems have been a key area of research. In the theory of slow-fast systems, the location of singular Hopf bifurcation and maximal canard is determined by computing the first Lyapunov coefficient. In particular, the analysis of canards is based on the genericity condition that the first Lyapunov coefficient must be non-zero. This manuscript aims to further extend the results to the case where the first Lyapunov coefficient vanishes. For that, the analytic expression of the second Lyapunov coefficient and the investigation of the normal form for codimension-2 singular Bautin bifurcation in a predator-prey system is done by explicitly identifying the locally invertible parameter-dependent transformations. A planar slow-fast predator-prey model with Holling type III functional response is considered here, where the prey population growth is affected by the weak Allee effect, and the prey reproduces much faster than the predator. Using geometric singular perturbation theory, normal form theory of slow-fast systems, and blow-up technique, we provide a detailed mathematical investigation of the system to show a variety of rich and complex nonlinear dynamics including but not limited to the existence of canards, relaxation oscillations, canard phenomena, singular Hopf bifurcation, and singular Bautin bifurcation. Additionally, numerical simulations are conducted to support the theoretical findings.

math.DS↗

arXiv2023

Structural sensitivity of chaotic dynamics in Hastings-Powell's model

The classical Hastings-Powell model is well known to exhibit chaotic dynamics in a three-species food chain. Chaotic dynamics appear through period-doubling bifurcation of stable coexistence limit cycle around an unstable interior equilibrium point. A specific choice of parameter value leads to a situation where the chaotic attractor disappears through a collision with an unstable limit cycle. As a result, the top predator goes to extinction. Here we explore the structural sensitivity of this phenomenon by replacing the Holling type II functional responses with Ivlev functional responses. Here we prove the existence of two Hopf-bifurcation thresholds and numerically detect the existence of an unstable limit cycle. The model with Ivlev functional responses does not indicate any possibility of extinction of the top predator. Further, the choice of functional responses depicts a significantly different picture of the coexistence of the three species involved with the model.

math.DS↗

arXiv2023

Spatio-temporal dynamics in a diffusive Bazykin model: effects of group defense and prey-taxis

Mathematical modeling and analysis of spatial-temporal population distributions of interacting species have gained significant attention in biology and ecology in recent times. In this work, we investigate a Bazykin-type prey-predator model with a non-monotonic functional response to account for the group defense among the prey population. Various local and global bifurcations are identified in the temporal model. Depending on the parameter values and initial conditions, the temporal model can exhibit long stationary or oscillatory transient states due to the presence of a local saddle-node bifurcation or a global saddle-node bifurcation of limit cycles, respectively. We further incorporate the movement of the populations consisting of a diffusive flux modelling random motion and an advective flux modelling group defense-induced prey-taxis of the predator population. The global existence and boundedness of the spatio-temporal solutions are established using $L^p$-$L^q$ estimate. We also demonstrate the existence of a non-homogeneous stationary solution near the Turing thresholds using weakly nonlinear analysis. A few interesting phenomena, which include extinction inside the Turing region, long stationary transient state, and non-homogeneous oscillatory solutions inside the Hopf region, are also identified.

math.DS↗

arXiv2023

Dynamics of infectious diseases in predator-prey populations: a stochastic model, sustainability, and invariant measure

This paper introduces an innovative model for infectious diseases in predator-prey populations. We not only prove the existence of global non-negative solutions but also establish essential criteria for the system's decline and sustainability. Furthermore, we demonstrate the presence of a Borel invariant measure, adding a new dimension to our understanding of the system. To illustrate the practical implications of our findings, we present numerical results. With our model's comprehensive approach, we aim to provide valuable insights into the dynamics of infectious diseases and their impact on predator-prey populations.

q-bio.PE↗

arXiv2023

Saddle-Node Bifurcation of Periodic Orbit Route to Hidden Attractors in Nonlinear Dynamical Systems

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these attractors is still not fully understood. In this letter, we present the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. We show that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were performed to demonstrate the existence of hidden attractors in these systems. Despite the difficulties in identifying the suitable initial conditions from the appropriate basin of attraction, we performed experiments to detect hidden attractors in nonlinear electronic circuits. Our results provide new insights into the generation of hidden attractors in nonlinear dynamical systems.

nlin.CD↗

arXiv2023

Spatio-temporal chaos and clustering induced by nonlocal information and vaccine hesitancy in the SIR epidemic model

Human behavior, and in particular vaccine hesitancy, is a critical factor for the control of childhood infectious disease. Here we propose a spatio-temporal behavioral epidemiology model where the vaccine propensity depends on information that is non-local in space and in time. The properties of the proposed model are analysed under different hypotheses on the spatio-temporal kernels tuning the vaccination response of individuals. As a main result, we could numerically show that vaccine hesitancy induces the onset of many dynamic patterns of relevance for epidemiology. In particular we observed: behavior-modulated patterns and spatio-temporal chaos. This is the first known example of human behavior-induced spatio-temporal chaos in statistical physics of vaccination. Patterns and spatio-temporal chaos are difficult to deal with, from the Public Health viewpoint, hence showing that vaccine hesitancy can cause them could be of interest. Additionally, we propose a new simple heuristic algorithm to estimate the Maximum Lyapunov Exponent.

physics.soc-ph↗

arXiv2023

Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth

Allee effect in population dynamics has a major impact in suppressing the paradox of enrichment through global bifurcation, and it can generate highly complex dynamics. The influence of the reproductive Allee effect, incorporated in the prey's growth rate of a prey-predator model with Beddington-DeAngelis functional response, is investigated here. Preliminary local and global bifurcations are identified of the temporal model. Existence and non-existence of heterogeneous steady-state solutions of the spatio-temporal system are established for suitable ranges of parameter values. The spatio-temporal model satisfies Turing instability conditions, but numerical investigation reveals that the heterogeneous patterns corresponding to unstable Turing eigen modes acts as a transitory pattern. Inclusion of the reproductive Allee effect in the prey population has a destabilising effect on the coexistence equilibrium. For a range of parameter values, various branches of stationary solutions including mode-dependent Turing solutions and localized pattern solutions are identified using numerical bifurcation technique. The model is also capable to produce some complex dynamic patterns such as travelling wave, moving pulse solution, and spatio-temporal chaos for certain range of parameters and diffusivity along with appropriate choice of initial conditions Judicious choices of parametrization for the Beddington-DeAngelis functional response help us to infer about the resulting patterns for similar prey-predator models with Holling type-II functional response and ratio-dependent functional response.

math.DS↗

arXiv2022

Attractors and long transients in a spatio-temporal slow-fast Bazykin's model

Spatio-temporal complexity of ecological dynamics has been a major focus of research for a few decades. Pattern formation, chaos, regime shifts and long transients are frequently observed in field data but specific factors and mechanisms responsible for the complex dynamics often remain obscure. An elementary building block of ecological population dynamics is a prey-predator system. In spite of its apparent simplicity, it has been demonstrated that a considerable part of ecological dynamical complexity may originate in this elementary system. A considerable progress in understanding of the prey-predator system's potential complexity has been made over the last few years; however, there are yet many questions remaining. In this paper, we focus on the effect of intraspecific competition in the predator population. In mathematical terms, such competition can be described by an additional quadratic term in the equation for the predator population, hence resulting in the variant of prey-predator system that is often referred to as Bazykin's model. We pay a particular attention to the case (often observed in real population communities) where the inherent prey and predator timescales are significantly different: the property known as a `slow-fast' dynamics. Using an array of analytical methods along with numerical simulations, we provide comprehensive investigation into the spatio-temporal dynamics of this system. In doing that, we apply a novel approach to quantify the system solution by calculating its norm in two different metrics such as $C^0$ and $L^2$. We show that the slow-fast Bazykin's system exhibits a rich spatio-temporal dynamics, including a variety of long exotic transient regimes that can last for hundreds and thousands of generations.

math.DS↗

arXiv2022

Pattern alternations induced by nonlocal interactions

Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the long-range diffusion occurs, and the usual reaction-diffusion (RD) model can not capture such phenomena. The nonlocal RD model, on the other hand, can fill the gap. Analytical derivation of the amplitude equations (AE) for an RD system is a valuable tool to predict the pattern selections, in particular, the stationary Turing patterns when they occur. In this paper, we analyze the conditions for the Turing bifurcation for the nonlocal model and also derive the AE for the nonlocal RD model near the Turing bifurcation threshold to describe the reason behind the pattern selections. This derivation of the AE is not only limited to the nonlocal prey-predator model, as shown in our representative example but also can be applied to other nonlocal models near the Turing bifurcation threshold. The analytical prediction agrees with numerical simulation near the Turing bifurcation threshold. Moreover, the analytical and numerical results fit each other well even more remote from the Turing bifurcation threshold for the small values of the nonlocal parameter but not for the higher values.

math.DS↗

arXiv2021

Bifurcation analysis of the predator-prey model with the Allee effect in the predator

The use of predator-prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka-Volterra system towards more realistic descriptions of the processes of predation, reproduction and mortality. One important aspect is the recognition of the fact that the growth of a population can be subject to an Allee effect, where the per capita growth rate increases with the population density. Including an Allee effect has been shown to fundamentally change predator-prey dynamics and strongly impact species persistence, but previous studies mostly focused on scenarios of an Allee effect in the prey population. Here we explore a predator-prey model with an ecologically important case of the Allee effect in the predator population where it occurs in the numerical response of predator without affecting its functional response. Biologically, this can result from various scenarios such as a lack of mating partners, sperm limitation and cooperative breeding mechanisms, among others. Unlike previous studies, we consider here a generic mathematical formulation of the Allee effect without specifying a concrete parameterisation of the functional form, and analyse the possible local bifurcations in the system. Further, we explore the global bifurcation structure of the model and its possible dynamical regimes for three different concrete parameterisations of the Allee effect. The model possesses a complex bifurcation structure: there can be multiple coexistence states including two stable limit cycles. Inclusion of the Allee effect in the predator generally has a destabilising effect on the coexistence equilibrium. We also show that regardless of the parametrisation of the Allee effect, enrichment of the environment will eventually result in extinction of the predator population.

q-bio.PE↗