Priority and age specific vaccination algorithm for the pandemic diseases: a comprehensive parametric prediction model

Background There have been several destructive pandemic diseases in the human history. Since these pandemic diseases spread through human-to-human infection, a number of non-pharmacological policies has been enforced until an effective vaccine has been developed. In addition, even though a vaccine has been developed, due to the challenges in the production and distribution of the vaccine, the authorities have to optimize the vaccination policies based on the priorities. Considering all these facts, a comprehensive but simple parametric model enriched with the pharmacological and non-pharmacological policies has been proposed in this study to analyse and predict the future pandemic casualties. Method This paper develops a priority and age specific vaccination policy and modifies the non-pharmacological policies including the curfews, lockdowns, and restrictions. These policies are incorporated with the susceptible, suspicious, infected, hospitalized, intensive care, intubated, recovered, and death sub-models. The resulting model is parameterizable by the available data where a recursive least squares algorithm with the inequality constraints optimizes the unknown parameters. The inequality constraints ensure that the structural requirements are satisfied and the parameter weights are distributed proportionally. Results The results exhibit a distinctive third peak in the casualties occurring in 40 days and confirm that the intensive care, intubated, and death casualties converge to zero faster than the susceptible, suspicious, and infected casualties with the priority and age specific vaccination policy. The model also estimates that removing the curfews on the weekends and holidays cause more casualties than lifting the restrictions on the people with the chronic diseases and age over 65. Conclusion Sophisticated parametric models equipped with the pharmacological and non-pharmacological policies can predict the future pandemic casualties for various cases.

A Short Inroad to Optimized Compactification of Composite Neutronic Shields

Compact neutronic shields for mobile nuclear reactors or accelerator-based neutron beams are known to be optimized multilayered composites. This paper is a simplified short inroad to the complex problem of optimizing the design of such shields when they attenuate a neutron beam to extremise certain quality criteria, in plane geometry, subject to equality and inequality constraints. In the equality constraints, the interfacial polychromatic neutron fluxes are solutions to course-mesh finite-difference holonomic state equations. The set of these interfacial fluxes act as state variables,while the set of layer thicknesses, or their poisoning (by added neutron absorbers) concentrations are decision variables. The entire procedure is then demonstrated to be reducible to standard Kuhn-Tucker semi-linear programming that may also lead robustly to an optimal sequence for these layers.

Generalization of the order-restricted information criterion for multivariate normal linear models (pre-print )

The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints.Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic.We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints.If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion.Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model.

An Akaike-type information criterion for model selection under inequality constraints (pre-print)

The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints. Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic. We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints. If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion. Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model.

Synchronization of Chaotic Systems: A Generic Nonlinear Integrated Observer-Based Approach

The purpose of this research is to study the synchronization of two integrated nonlinear systems with time delay and disturbances. A nonlinear system is a system in which the difference in output is not relative to the difference in input. A new control methodology for synchronization of the two chaotic systems master and slave is recognized by means of the unique integrated chaotic synchronous observer and the integrated chaotic adaptive synchronous observer. The instantaneous approximation states of the master and slave systems are accomplished by means of methods for suggesting observers for every one of the master and slave systems and by the production of error signals between these approximated states. This approximated synchronization error signal and state approximation errors meet at the origin by means of methods involving a particular observer-based feedback control signal to ensure synchronization and state approximation. Using Lyapunov stability theory, adaptive and nonadaptive laws for control systems, and nonlinear properties, the intermingling conditions for state approximation errors and approximated synchronization errors are established as nonlinear matrix inequalities. A solution to the resulting inequality constraints using a two-step linear matrix inequality (LMI)-based approach is introduced, giving essential and adequate conditions to extract values from the controller gain and observer gain matrices. Simulation of the suggested synchronization procedure for FitzHugh–Nagumo neuronal systems is demonstrated to expand the viability of the suggested observer-based control techniques.

Approximation of value function of differential game with minimal cost

The paper is concerned with the approximation of the value function of the zero-sum differential game with the minimal cost, i.e., the differential game with the payoff functional determined by the minimization of some quantity along the trajectory by the solutions of continuous-time stochastic games with the stopping governed by one player. Notice that the value function of the auxiliary continuous-time stochastic game is described by the Isaacs–Bellman equation with additional inequality constraints. The Isaacs–Bellman equation is a parabolic PDE for the case of stochastic differential game and it takes a form of system of ODEs for the case of continuous-time Markov game. The approximation developed in the paper is based on the concept of the stochastic guide first proposed by Krasovskii and Kotelnikova.

A trim problem formulation for maximum control authority using the Attainable Moment Set geometry

This paper presents a generic trim problem formulation, in the form of a constrained optimization problem, which employs forces and moments due to the aircraft control surfaces as decision variables. The geometry of the Attainable Moment Set (AMS), i.e. the set of all control forces and moments attainable by the control surfaces, is used to define linear equality and inequality constraints for the control forces decision variables. Trim control forces and moments are mapped to control surface deflections at every solver iteration through a linear programming formulation of the direct Control Allocation algorithm. The methodology is applied to an innovative box-wing aircraft configuration with redundant control surfaces, which can partially decouple lift and pitch control, and allow direct lift control. Novel trim applications are presented to maximize control authority about the lift and pitch axes, and a “balanced” control authority. The latter can be intended as equivalent to the classic concept of minimum control effort. Control authority is defined on the basis of control forces and moments, and interpreted geometrically as a distance within the AMS. Results show that the method is able to capitalize on the angle of attack or the throttle setting to obtain the control surfaces deflections which maximize control authority in the assigned direction. More conventional trim applications for minimum total drag and for assigned angle of elevation are also explored.