Asansol Girls' College

In this article, we extended the basic Susceptible-Exposed-Infectious-Quarantined-Hospitalized-Recovered (SEIQHR) compartmental model to the Susceptible-Exposed-Infectious-Quarantined-Hospitalized-Recovered-Awareness (SEIQHRA) framework by incorporating the level of awareness, A, as an additional model population to gain deeper insights into the dynamic process of infectious disease outbreaks, with particular emphasis on awareness-based interventions. Hospitalization, treatment, and quarantining procedures informed by awareness were integrated into this refined model. We investigated the key mathematical properties including boundedness of solutions, the basic reproduction number, and the existence of equilibriums. The model admitted two equilibria: The disease-free and the endemic equilibrium. The disease-free equilibrium was shown to be globally asymptotically stable when R-0 < 1 and unstable when R-0 > 1. Forward bifurcation occurred at R-0 = 1. The endemic equilibrium underwent a Hopf bifurcation, resulting in a stability switch. To design effective awareness-based interventions, the Pontryagin maximum principle was employed to derive optimal control parameters. Numerical simulations were conducted to validate the analytical findings, highlighting the role of awareness-driven control measures in controlling an infectious disease and enhancing public health outcomes.

We investigate the nonequilibrium dynamics of a two-dimensional rotating Bose gas confined in a symmetric anharmonic trap, employing the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We study states ranging from vortex-free configurations to multicharged (giant) vortices, prepared by tuning the rotation frequency, and analyze their response to sudden interaction and trap quenches. In vortex-free states, interaction quenches induce regular breathing–like dynamics, whereas in the presence of giant vortices they lead to symmetry-breaking surface excitations. In contrast, trap deformations that excite quadrupole-like modes produce stable oscillations in vortex-free condensates but trigger rapid, irregular, and effectively chaotic splitting dynamics in multicharged vortices. To characterize these processes beyond conventional density and phase observables, we employ information-theoretic measures, including marginal and joint entropies, mutual information, and Kullback-Leibler (KL) divergence, supplemented by an angular-resolved KL measure that captures symmetry breaking and azimuthal localization. We find that chaotic splitting is accompanied by a pronounced growth of information-theoretic indicators, signaling the buildup of many-body correlations and increasing complexity in the system dynamics. Our results demonstrate the extreme sensitivity of giant vortices to excitation protocols and establish information-theoretic measures as a powerful framework to quantify correlations and complexity in rotating quantum gases.

Cancer arises from intricate interactions among tumor cell proliferation, immune system dynamics, and therapeutic interventions. In this study, we develop a mathematical model that incorporates tumor growth, immune stimulation and suppression, as well as drug dynamics. The disease-free and endemic equilibria, and the basic reproduction number (R0) are computed to study the dynamics of the disease. Stability analysis is conducted to determine the conditions under which malignant cells either persist or are eradicated. Furthermore, the model is extended by introducing an optimal control parameter for drug infusion, with Pontryagin’s Maximum Principle applied to characterize the optimal therapeutic strategy. This study shows the theoretical insights into the delicate balance between tumor suppression and immune exhaustion, thereby providing guidance for the design of an effective treatment strategy.

Exopolysaccharides (EPS) synthesized by rhizospheric bacteria of the rhizophytes have emerged as critical biomolecules for enhancing plant resilience to environmental stressors. These high-molecular-weight polymers contribute to soil aggregation, water retention, nutrient absorption, and biofilm formation, which collectively improve plant health and yield under challenging conditions such as drought, salinity, extreme temperatures, and heavy metal contamination. This review synthesizes insights from recent studies to provide a comprehensive perspective on the structure, biosynthesis, and functional roles of bacterial EPS. Emphasis is placed on the mechanisms through which EPS facilitate stress tolerance, the regulatory processes underlying their production, and their application in sustainable agriculture. This review highlights the role of EPS-producing bacterial strains in mitigating various abiotic stresses, emphasizing their potential mechanisms and applications. It further discusses the levels of EPS production across different strains and provides examples of plants harboring rhizophytes associated with such beneficial bacteria. By consolidating findings from diverse studies, this work underscores the significance of EPS as a key component of microbe-mediated plant protection and an alternative to chemical-based agricultural inputs.

In this research, we have derived a mathematical model to study the impact of health center-based awareness campaigns on the spread of human papillomavirus (HPV) infection to cervical cancer. In the model, the human population is divided into susceptible, vaccinated, permanently immune, infected with HPV, and recovered. Moreover, awareness level is assumed as a model compartment. The awareness level affects the rates of infection, vaccination, recovery, and disease progression. The basic reproduction number (R-0) is calculated using the next-generation matrix method. The equilibrium points are determined, and their stability analysis is conducted. Disease-free equilibrium (DFE) is globally asymptotically stable for R-0< 1. Forward transcritical bifurcation occurs at R-0 = 1. Furthermore, optimal control theory is employed using Pontryagin's maximum principle, with the objective of minimizing infection rates through optimal vaccination at the minimum cost of control. These results are validated by numerical simulations. The results show that effective HPV awareness campaigns can help control the spread of HPV infections, making it easier to manage cervical cancer. This study confirms the importance of awareness-induced behavioral dynamics in modeling spread of HPV for efficient disease management. Awareness campaigns with optimal vaccination can significantly lower HPV transmission and reduce the incidence of cervical cancer.