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In this paper, we propose a compartmental epidemic model which consists of four divisions named as non-quarantined susceptible population (S„). quarantined susceptible population (S9), infected population (I), and recovered or immune population (R) to analyze the dynamics of pandemic disease COVID 19 introducing a time delay. We analytically calculate the basic reproduction number of the model to classify epidemic case and endemic case of the pandemic. In order to understand the dynamics of Novel Coronavirus under a time delay, we perform the stability analysis and a Hopfbifurcation analysis of the proposed model as well. Finally, numerical simulations are performed to illustrate the analytical findingsthat reflect a real scenario of the transmission of COVID-19. [ABSTRACT FROM AUTHOR]

In this paper, we argue that in terms of spatiotemporal fluctuations non population density, the genuine allelopathic prey-predator system is typically inhomogeneous. With this in mind, we add noise to the system to simulate the effect of environmental heterogeneity on prey-predator interactions. The noise analysis of the system suggests the impression of the environmental pollution on the dynamical behavior of solutions. We mainly focused on the importance of stochastic coefficient, diffusion coefficient and its possible ergodic behavior in a time dependent and time independent prey population density problem is taken under consideration in the study. [ABSTRACT FROM AUTHOR]

This article presents an artificial drug abusers system consolidating the impact of treatment with psychological and physiological addicts under fuzzy parameters. In the fuzzy model, all of the parameters are considered to be triangular fuzzy numbers to represent the uncertainty that pervaded the dynamics. To handle the arrangements while avoiding problems, the fuzzy model is turned into a defuzzified model using the utility function method. The fuzzy model's positivity and boundedness are carefully explored, and an equilibrium analysis is also completed. Both the drug-addict equilibrium and the drug-free equilibrium have established stability analyses. This article explains fuzzy optimum control using Pontryagin's maximum principle. Finally, it is shown that the treatment alongside counselling and conducting awareness programs is more fruitful and drug-related controlling is more viable in the fuzzy nature. Likewise, we plot the 3D associations with fuzzy parameters which show the inventiveness and appropriateness of the results. [ABSTRACT FROM AUTHOR]

As we know from theory of evolution in ecology that the generalist predators feed on a variety of prey species may tend to persist in an ecosystem even if one particular prey species is absent in that environment. Predation by generalist predators is followed by a sigmoidal functional response which is ensured in literature. We already know that a mathematical predator-prey type model with sigmoidal functional response is found to be more realistic and stable than for a Holling type II functional response. In our model the generalist predator may go to extinct in the absence of one focal prey. It's dynamics are studied in terms of the local and global aspect and stabilities are verified around the positive equilibrium with the impact of constant delay in the functional response term as some time will be required for gestation of prey for predators. The condition for Hopf-bifurcation of the system has been derived. Numerical computer simulations have been done and compared with the analytical results of the model analysis. [ABSTRACT FROM AUTHOR]