In this paper, we have considered a dynamical model of diseases that spread by droplet infection and also through direct contact with varying total population size and discrete time delay to become infectious. It is assumed that there is a latent period of the disease and an immune period of the recovered individuals. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analysed this model with pulse vaccination and saturation incidence rate. It is also assumed that the time lag due to lose of immunity of recovered individuals is equal to the interval between two pulses. We have defined two positive numbers R 1 and R 2. It is proved that there exists an infection-free periodic solution which is globally attractive if R 1 < 1 and the disease is permanent if R 2 > 1. The important mathematical findings for the dynamical behaviour of the model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.

This paper aims to study the dynamical behaviours of a prey-predator system, where both the prey and predator show herd behaviours. Positivity, boundedness, stability of equilibrium points, et cetera, are discussed in deterministic environment. To incorporate the effect of fluctuating environment, we have perturbed the birth rate of prey species and death rate of predator species by Gaussian white noises. Then the resulting model is cultured by the method of statistical linearization to study the stability and non-equilibrium fluctuation of the populations in stochastic environment. Numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically. ARTICLE HISTORY

In this paper we have studied the dynamical behaviours of an SIQR epidemiological model which takes into account the psychological effect introduced by a nonlinear and non-monotone incidence. Positivity and boundedness of the system have been studied. Stability analysis of the equilibrium points is presented. We have carried out numerical simulations to validate the analytical findings. The biological implications of our analytical and numerical findings are discussed.

In this work we have studied the deterministic behaviours of a competition model with herd behaviour and Allee effect. The uniform boundedness of the system has been studied. Criteria for local stability at equilibrium points are derived. The effect of discrete time-delay on the model is investigated. We have carried out numerical simulations to validate the analytical findings. The biological implications of our analytical and numerical findings are discussed.

<p>In this work, we report a large-area fabrication of a flexible superhydrophobic bactericidal surface decorated with copper hydroxide nanowires. This involves a simple two-step method which involves growth followed by transfer of the nanowires onto the polydimethylsiloxane (PDMS) surface by mechanical peeling. Additional roughness in PDMS is obtained through incomplete wetting of the nanoscale gaps which leads to multi-scale superhydrophobicity with contact angle of 169° and hysteresis of less than 2°. The simplicity of the process makes it low-cost and easily scalable. The process allows fabrication of non-planar 3D surfaces. The surface shows blood repellence and antimicrobial activity against <i>E. coli </i>with<i> </i>more than 5 log reductions in bacterial colony. The surface also shows hemocompatible behaviour making it suitable for healthcare applications. The fabricated surface is found to be extremely robust against stretching, twisting, sand paper abrasion, solid weight impact, and tape peel test. The surface is found to withstand human weight multiple times without losing its hydrophobicity making it suitable for several practical scenarios in healthcare and household applications. </p>