Asansol Girl's College is a women's college in Asansol, Paschim Bardhaman district, West Bengal, India. It offers undergraduate courses in arts and sciences. The College is affiliated to Kazi Nazrul University, Asansol, West Bengal, India.
Plants possess innate resistance mechanisms, originating from their immune systems, to defend against pathogenic or viral invasions. This study presents a mathematical model, using nonlinear infection terms, designed to investigate plant resistance to mosaic virus, which is transmitted via whitefly vectors. The proposed model incorporates microbial biostimulants aimed at enhancing plant growth and stimulating immune responses to enhance disease resistance. Additionally, the model accounts for a time delay associated with the plant’s incubation period. The basic reproduction number, denoted as R_0 , is derived to characterize the system’s dynamics. Equilibrium points are identified, and their stability properties are rigorously analyzed. The influence of various parameters related to disease resistance is examined through both analytical and numerical approaches. The analysis reveals that the disease-free equilibrium remains stable when R_0 < 1 . In contrast, an endemic equilibrium emerges when R_0 > 1 , and the system exhibits Hopf bifurcation as a key parameter exceeds its critical threshold. Bubbling phenomena are observed when variations occur in the resistance rate and incubation period. The findings demonstrate that both the resistance rate and the application of microbial biostimulants play a stabilizing role in disease dynamics and enhance plant growth, whereas an increased infection rate tends to destabilize the system. Therefore, the results can help farmers with a strategic advantage in managing plant disease, crop health, and increasing crop productivity.
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.
