In this study based on Bangladesh, a modified SIR model is produced and analysed for COVID-19. We have theoretically investigated the model along with numerical simulations. The reproduction number
has been calculated by using the method of the next-generation matrix. Due to the basic reproduction number, we have analysed the local stability of the model for disease-free and endemic equilibria. We have investigated the sensitivity of the reproduction number to parameters and calculate the sensitivity indices to determine the dominance of the parameters. Furthermore, we simulate the system in MATLAB by using the fourth-order Runge–Kutta (RK4) method and validate the results using fourth order polynomial regression (John Hopkins Hospital (JHH), 2020). Finally, the numerical simulation depicts the clear picture of the upward, and the downward trend of the spread of this disease along with time in a particular place, and the parameters in the mathematical model indicate this change of intensity. This result represents, the effect of COVID-19 from Bangladesh’s perspective.
Considering a gravitational coupling between the spin and the orbital angular momentum of a spinning test particle orbiting a central massive body, we derive two particular consequences: (1) the influence of the coupling on the location of the innermost stable circular orbit and (2) the gravitomagnetic clock effect due to this coupling. The previous result does not seem to exist for the former, while for the latter we arrive at a result that coincides with what we think is the most accurate.
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
Genetic networks play a fundamental role in the regulation and control of the development and function of organisms. A simple model of gene networks assumes that a gene can be switched on or off as regulatory inputs to the gene cross critical thresholds. In studies of dynamics of such networks, we found unusual dynamical behavior in which phase plane trajectories display irregular dynamics that shrink over long times. This observation leads us to identify a type of dynamics, that can be described as collapsing chaos, in which the Lyapunov exponent is positive, but points on the trajectory approach the origin in the long time limit.
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