Dynamical behaviours and stability analysis of a generalized fractional model with a real case study.

INTRODUCTION: Mathematical modelling is a rapidly expanding field that offers new and interesting opportunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. OBJECTIVES: The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. METHODS: The new model in this paper is formulated in the Caputo sense, employs a nonlinear time-varying transmission rate, and consists of ten population classes including susceptible, infected, diagnosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical behaviours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated. RESULTS: Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied. CONCLUSION: According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.

Experimental and numerical evaluation of a novel dual-channel windcatcher with a rotary scoop for energy-saving technology integration

With the increasing requirements for fresh air supply in buildings after the COVID-19 pandemic and the rising energy demand from buildings, there has been an increased emphasis on passive cooling techniques such as natural ventilation. While natural ventilation devices such as windcatchers can be a sustainable and low-cost solution to remove indoor pollutants and improve indoor air quality, it is not as reliable as mechanical systems. Integration with low-energy cooling, heating or heat recovery technologies is necessary for operation in unfavourable outdoor conditions. In this research, a novel dual-channel windcatcher design consisting of a rotary wind scoop and a chimney was proposed to provide a fresh air supply irrespective of the wind direction. The dual-channel design allows for passive cooling, dehumidification and heat recovery technology integration to enhance its thermal performance. In this design, the positions of the supply and return duct are "fixed” or would not change under changing wind directions. An open wind tunnel and test room were employed to experimentally evaluate the ventilation performance of the proposed windcatcher prototype. A Computational Fluid Dynamic (CFD) model was developed and validated to further evaluate the system's ventilation performance. The results confirmed that the system could supply sufficient fresh air and exhaust stale air under changing wind directions. The ventilation rate of the rotary scoop windcatcher was higher than that of a conventional 8-sided multidirectional windcatcher of the same size. © 2023 The Author(s)

COVID-19 SPATIOTEMPORAL SIR MODEL: REGIONAL OPTIMAL CONTROL APPROACH

In the present work, we consider a spatio-temporal model to describe the evolution of covid19 in an area Ω (Ω can be a city, a country,..). Taking into account the financial means of the considered country, we suppose that the number of available vaccines is destined to a region ω1 ⊆Ω (ω1 can be an industrial city, a university city. ..) and we suppose that the available treatments are dedicated to a region ω2 ⊆ Ω (ω2 can be a military city,..), it is not excluded that ω1 = ω2 . To minimize the number of infection with minimal cost, we apply an optimal regional control strategy to stop the death of infected individuals in the considered area. Much of this work has been devoted to mathematical study, where the existence of the optimal controls and the solutions of the state system are proven, an optimal control characterization in terms of state and adjoint functions are provided, and the optimality system is solved numerically using a forward-backward sweep method. Our numerical results suggest that when vaccination and treatment procedures are used together, the control approach becomes more effective in protecting a specific region from epidemic transmission from neighboring regions. © 2022 the author(s).

The Impact of Delay Strategies on the Dynamics of Coronavirus Pandemic Model with Nonlinear Incidence Rate

Currently, the world is facing a devastating pandemic of a novel coronavirus, which started as an outbreak of pneumonia of unknown cause in Wuhan city of China in December of 2019. According to the recent report of the World Health Organization (WHO), 210 countries convicted badly 1.8 million infections and almost 200,000 causalities. Due to the non-availability of the vaccination, delay strategies such as community distancing, travel restrictions, extension in breaks, use of face-mask, and self-quarantine are the effective treatments to control the pandemic of coronavirus. So, we proposed the delayed susceptible-exposed-infected-recovered model with a nonlinear incidence rate to study the effective role of control strategies. For this analysis, we discussed three types of equilibria of the model such as trivial, coronavirus free, and coronavirus existence with delay terms. The local and global stabilities are investigated by using well-posed notations like the Lasalle invariance principle, Routh-Hurwitz criterion, and Lyapunov function. In the end, some useful replications are presented.

Fractal-fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling.

The fractal-fraction derivative is an advanced category of fractional derivative. It has several approaches to real-world issues. This work focus on the investigation of 2nd wave of Corona virus in India. We develop a time-fractional order COVID-19 model with effects of disease which consist system of fractional differential equations. Fractional order COVID-19 model is investigated with fractal-fractional technique. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. Fractional order system is analyzed qualitatively as well as verify sensitivity analysis. The existence and uniqueness of the fractional-order model are derived using fixed point theory. Also proved the bounded solution for new wave omicron. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the actual behavior of the OMICRON virus. Such kind of analysis will help to understand the behavior of the virus and for control strategies to overcome the disseise in community.

An Approximate Numerical Methods for Mathematical and Physical Studies for Covid-19 Models

The advancement in numerical models of serious resistant illnesses is a key research territory in different fields including the nature and the study of disease transmission. One of the aims of these models is to comprehend the elements of conduction of these infections. For the new strain of Covid-19 (Coronavirus), there has been no immunization to protect individuals from the virus and to forestall its spread so far. All things being equal, control procedures related to medical services, for example, social distancing or separation, isolation, and travel limitations can be adjusted to control this pandemic. This article reveals some insights into the dynamic practices of nonlinear Coronavirus models dependent on the homotopy annoyance strategy (HPM). We summon a novel sign stream chart that is utilized to depict the Coronavirus model. Through the numerical investigations, it is uncovered that social separation of the possibly tainted people who might be conveying the infection and the healthy virus-free people can diminish or interrupt the spread of the infection. The mathematical simulation results are highly concurrent with the statistical forecasts. The free balance and dependability focus for the Coronavirus model is discussed and the presence of a consistently steady arrangement is demonstrated. © 2022 CRL Publishing. All rights reserved.

Review of fractional epidemic models.

The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.

Effectively managing diagnostic tests to monitor the COVID-19 outbreak in Italy.

Urged by the outbreak of the COVID-19 in Italy, this study aims at helping to tackle the spread of the disease by resorting to operations research techniques. In particular, we propose a mathematical program to model the problem of establishing how many diagnostic tests the Italian regions must perform in order to maximize the overall disease detection capability. An important feature of our approach is its simplicity: data we resort to are easy to obtain and one can employ standard optimization tools to address the problem. The results we obtain when applying our method to the Italian case seem promising.