1. Control Methodology 2. Dynamical Systems 3. Applications to Social and Environmental Problems

Dynamics and Control

This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points are given, namely the disease-free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. By constructing suitable Lyapunov functional, the global stability of the disease-free equilibrium is proved depending on the basic reproduction number 
$$R_0$$

. Furthermore, using other appropriate Lyapunov functionals, the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number 
$$R^{1}_0$$

 and the strain 2 reproduction number 
$$R^{2}_0$$

. Numerical simulations are performed in order to confirm the different theoretical results. It was observed that the model with a generalized incidence functions encompasses a large number of models with classical incidence functions and it gives a significant wide view about the equilibria stability. Numerical comparison between the model results and COVID-19 clinical data was conducted. Good fit of the model to the real clinical data was remarked. The impact of the quarantine strategy on controlling the infection spread is discussed. The generalization of the problem to a more complex compartmental model is illustrated at the end of this paper.

/pdf/global-dynamics-of-a-multi-strain-seir-epidemic-model-with-3bmyvhq936.pdf

Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic.

Abstract General, or private and non-commercial, aviation accidents produce more fatalities than any other aviation category within the United States. Despite advances in scientific understanding and technology since the early 1900s, weather causes concern for aviation safety, and little is known about the characteristics of fatal weather-related general aviation accidents. We provide a comprehensive spatiotemporal analysis of fatal weather-related general aviation accidents from 1982 through 2013 using data culled from the United States National Transportation Safety Board (NTSB). Weather was a cause or contributing factor in 35% of fatal general aviation accidents, of which 60% occurred while instrument meteorological conditions were present. Fatal weather-related general aviation accidents occur most frequently between October and April, on weekends, in early morning and evening periods, and along the West Coast, Colorado Rockies, Appalachian Mountains, and the Northeast. There has been a long-term reduction in weather-related general aviation accidents and fatalities since the 1980s; nonetheless, these accidents are still responsible for nearly 100 fatalities/year in the United States. This study provides pilots, academics, the Federal Aviation Administration, the NTSB, and other aviation organizations with information to advance mitigation efforts aimed at reducing future aviation-related accidents in the United States.

Fatal weather-related general aviation accidents in the United States: 1982 -- 2013

The outbreak of COVID-19 caused by SARS-CoV-2 in Wuhan and other cities in China in 2019 has become a global pandemic as declared by World Health Organization (WHO) in the first quarter of 2020 . The delay in diagnosis, limited hospital resources and other treatment resources leads to rapid spread of COVID-19. In this article, we consider an optimal control COVID-19 transmission model and assess the impact of some control measures that can lead to the reduction of exposed and infectious individuals in the population. We investigate three control strategies for this deadly infectious disease using personal protection, treatment with early diagnosis, treatment with delay diagnosis and spraying of virus in the environment as time-dependent control functions in our dynamical model to curb the disease spread.

Controlling the Transmission Dynamics of COVID-19

34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.The online version supplementary material available at 10.1007/s11071-022-07235-7. 

/pdf/mathematical-modeling-and-optimal-intervention-strategies-of-3qqgz2d6.pdf

Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

World Health Organization (WHO) has declared COVID-19 a pandemic on March 11, 2020 As of May 23, 2020, according to WHO, there are 213 countries, areas or territories with COVID-19 positive cases To effectively address this situation, it is imperative to have a clear understanding of the COVID-19 transmission dynamics and to concoct efficient control measures to mitigate/contain the spread In this work, the COVID-19 dynamics is modelled using susceptible-exposed-infectious-removed model with a nonlinear incidence rate In order to control the transmission, the coefficient of nonlinear incidence function is adopted as the Governmental control input To adequately understand the COVID-19 dynamics, bifurcation analysis is performed and the effect of varying reproduction number on the COVID-19 transmission is studied The inadequacy of an open-loop approach in controlling the disease spread is validated via numerical simulations and a robust closed-loop control methodology using sliding mode control is also presented The proposed SMC strategy could bring the basic reproduction number closer to 1 from an initial value of 25, thus limiting the exposed and infected individuals to a controllable threshold value The model and the proposed control strategy are then compared with real-time data in order to verify its efficacy

/pdf/dynamics-and-control-of-covid-19-pandemic-with-nonlinear-whec76wsow.pdf

Dynamics and control of COVID-19 pandemic with nonlinear incidence rates.

High-frequency control switching, chattering, limits the practical application of sliding mode controllers. This paper proposes an enhanced reaching law, viz., Fractional Power Rate Reaching Law (FPRRL), for the design of sliding mode controllers to mitigate the chattering problem. Controller gains are selected to accommodate variations in switching function dynamically to prevent over-actuation near the sliding surface, which is the primary reason for chattering. Chattering mitigation is achieved without compromising other attributes of sliding mode control. Performance enhancements in the attributes, viz., reaching time, robustness, and reduced chattering magnitude have been established through the methodical analysis of the new reaching law. The proposed control strategy is then bench-marked with the state of the art reaching law methods through simulations by considering a twin-rotor MIMO system control problem.

Fractional power rate reaching law for augmented sliding mode performance

This article presents a string stable controller for the autonomous operation of a platoon of Heavy Commercial Road Vehicles (HCRVs) in a connected environment. This study considers factors such as brake/powertrain actuator dynamics, resistive forces, tyre model and wheel dynamics, which are crucial during on-road operation of HCRVs. A nonlinear vehicle dynamic model encompassing all these factors has been considered. The dependency between aerodynamic drag and inter-vehicular distance in the platoon has also been taken into account. The aforementioned factors motivated the use of Sliding Mode Control (SMC), which is a nonlinear and robust control technique. A lower level Proportional Integral Derivative (PID) controller has been successfully integrated with SMC to compensate for pneumatic brake and powertrain system delay. The designed controller was evaluated for string stable platoon operation by considering various road conditions, load conditions and operating speeds. It was observed that the string stable controller performance is highly dependent on the operating conditions. To ensure string stable operation for different operating scenarios, an adaptive time-headway based enhancement has also been integrated in the controller design. The efficacy of the proposed adaptive time-headway policy over the existing constant time-headway policy has been methodically analysed and a performance comparison between them has also been presented. The aspect of communication delay during connected vehicular operation has also been studied and the maximum tolerable communication delay magnitude for maintaining string stable operation has also been presented.

/pdf/a-dynamics-based-adaptive-string-stable-controller-for-408y12zupv.pdf

A Dynamics-Based Adaptive String Stable Controller for Connected Heavy Road Vehicle Platoon Safety

Aircraft loss of control is an acute phenomenon that has far reaching consequences irrespective of the class and type of aircraft. In order to ensure safe aircraft operation, loss of control proble...

An investigation into aircraft loss of control and recovery solutions

Integration of heavy commercial road vehicle platooning concept and electric vehicle technology is a promising approach as far as sustainable freight transportation is considered. This article atte...

G. Rohith

Papers

Dynamics and control of COVID-19 pandemic with nonlinear incidence rates.

Fractional power rate reaching law for augmented sliding mode performance

A Dynamics-Based Adaptive String Stable Controller for Connected Heavy Road Vehicle Platoon Safety

An investigation into aircraft loss of control and recovery solutions

String stable control of electric heavy vehicle platoon with varying battery pack locations