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In this study, we conduct a global stability analysis of an extended Susceptible-Unidentified infected-Confirmed (SUC) epidemic mathematical model. In the original SUC model, the entire population consists of individuals who are susceptible, those with unidentified infections, and those with confirmed infections, without accounting for births and deaths. In the proposed extended SUC model, we incorporate the dynamics of births and deaths into the original SUC model. We analyze the global stability of this extended SUC epidemic mathematical model and perform several computational experiments to validate the global stability analysis. Through this realistic extended SUC model, we aim to advance the current understanding of epidemiological modeling and provide valuable insights for guiding public health interventions and policies. [ABSTRACT FROM AUTHOR]

This paper explores the synergy between fuzzy set theory and genetic algorithms in the domain of epidemic modeling, shedding light on the broader challenges inherent in infectious diseases. In response to the evolving landscape of epidemiology, the study advocates for sophisticated modeling techniques to better understand and predict dynamic scenarios. The research thoroughly investigates the global stability of equilibrium solutions within a fuzzy epidemic model, accompanied by an inventive parameter estimation methodology. Utilizing Lyapunov functions, the paper establishes global stability outcomes for both disease-free and endemic equilibria. The novel approach, integrating continued fraction theory and a genetic algorithm, is applied to fit real-world epidemic data, offering insights crucial for public health planning and control measures. By addressing unexplored facets and bridging gaps in previous research, the paper contributes to a more comprehensive understanding of epidemic dynamics, providing a foundation for effective public health strategies in the face of infectious diseases.

A computational methodology is presented for calculating the spatial evolution of Tollmien–Schlichting (T–S) waves and their amplitude growth-rate factor in substantially nonparallel compressible flows, based on a global stability analysis of stationary solutions of the full Navier–Stokes (N–S) equations. Three stages of this methodology (obtaining a stationary solution, as well as carrying out a global stability analysis and its postprocessing) are described, and the results are presented of its validation based on the comparison of the results of calculating the characteristics of T–S waves on a flat plate with the corresponding results of the classical stability theory in the parallel approximation. An example of calculating the flow around a plate with a rectangular cavity is presented to illustrate the possibility of applying the proposed methodology to nonparallel flows. [ABSTRACT FROM AUTHOR]

The main buffet suppression techniques of aircrafts include active and passive flow control, aiming to reduce the impact of the fluctuating loads on the airfoil. These techniques are remedies after the airfoil design. The buffet suppression is not always considered in the aerodynamic optimization in the state of airfoil design because it is difficult to extract an appropriate key objective variable to indicate the flow stability. In this paper, the damping rate of disturbance, which is computed by the global stability analysis, can be used to indicate flow stability. Based on the global stability analysis, a transonic buffet suppression methodology by airfoil optimization is proposed. The objective is to improve the aerodynamic performance as well as the flow stability in the desired flight state. The RAE2822 airfoil is chosen as the initial airfoil. A benchmark of the unsteady aerodynamic configuration optimization design considering buffet suppression is developed. First, the numerical methods are verified and the damping rate of disturbance is chosen as a constraint in the aerodynamic optimization to extend the buffet onset. Then, the surrogate models constructed by the radial basis function interpolation are used to replace the computational fluid dynamics (CFD) solver. The teaching- and learning-based optimization (TLBO) is used. Finally, the aerodynamic and the flow stability characteristics of the airfoil before and after optimization are compared and analyzed. The proposed optimization framework can not only improve the aerodynamic characteristics in the cruise state but can also suppress the transonic buffet on higher angles of attack. [ABSTRACT FROM AUTHOR]

Staphylococcus aureus has been increasing globally, which negatively affects food safety, human and veterinary medicine. It colonizes about 30% of the world population, causing superficial skin and soft tissue infections. The dynamics of direct (human-to-human) and indirect (environment-to-human) transmission, shedding, and treatment failure of the disease remains an open epidemiological challenge. Therefore, this study introduces a mathematical model that incorporates both direct and indirect transmission cycle, effect of shedding, treatment failure and time-dependent control parameters. We derive an expression for the basic reproduction number, R0s, under different scenarios. Using comparison, Lyapunov and center manifold theories, we establish that the non-optimal control model is globally asymptotically stable whenever R0s

Fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. The framework here proposed is based on a Jacobian-free approach that enables GSA on large 3D grids, making this the first stability study on a full-aircraft at typical flight Reynolds numbers. The Reynolds-averaged Navier-Stokes solutions compare reasonably well with the available experiments and are used as base flows for the stability analyses. GSA is first performed at wind tunnel Reynolds number conditions, and a buffet-cell mode localized in the wing outboard region is found to be responsible for the onset. When the side-of-body (SOB) separation becomes larger at higher angles of attack, two additional modes are detected: a high-frequency mode localized in the SOB region and a low-frequency long-wavelength buffet-cell mode that may represent the link with the shock-oscillation instability found in two-dimensional airfoils. The existence of the buffet-cell mode is confirmed at flight Reynolds numbers. However, due to the presence of large SOB separation at the onset angle of attack, this mode is distributed along the whole wing and an SOB separation mode also appears. As well as characterizing buffet on industry-relevant geometries and flow conditions, this study proves that the proposed GSA framework is feasible for large 3D numerical grids and can represent a useful tool for buffet onset prediction during design and certification phases of commercial aircraft. [ABSTRACT FROM AUTHOR]

This paper explores a mathematical model of malaria, focusing on the basic reproduction number (R0) and employing Lyapunov functions to assess the global stability of disease-free and endemic equilibria. Sensitivity analysis of key parameters is conducted to evaluate their impact on disease control. The results indicate an active malaria outbreak with decreasing human classes signifying disease progression and increasing mosquito classes suggesting heightened transmission risk. Effective control measures, including mosquito control and treatment of infected individuals, are essential to mitigate the outbreak. [ABSTRACT FROM AUTHOR]

In the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydrodynamics simulation (in addition to the already existing CA). The DA was successfully verified by comparison between the obtained numerical result and that of solving the transient Navier–Stokes equations. The comparison of these approaches was carried out using the example of a laminar flow past a cylinder by a perfect gas at the near-critical Reynolds numbers (Re = 50 and 60). It was established that the CA predicted the growth rate of perturbations more accurately, while the DA did their frequency and amplitude in toto. The results obtained allow to assert that both CA and DA are equivalent in terms of accuracy, and the choice of a particular approach for analyzing the stability may be determined by other criteria, e. g., ease of implementation, computational work and so on.

Copyright of Guangdong Architecture Civil Engineering is the property of Guangdong Architecture Civil Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The main buffet suppression techniques of aircrafts include active and passive flow control, aiming to reduce the impact of the fluctuating loads on the airfoil. These techniques are remedies after the airfoil design. The buffet suppression is not always considered in the aerodynamic optimization in the state of airfoil design because it is difficult to extract an appropriate key objective variable to indicate the flow stability. In this paper, the damping rate of disturbance, which is computed by the global stability analysis, can be used to indicate flow stability. Based on the global stability analysis, a transonic buffet suppression methodology by airfoil optimization is proposed. The objective is to improve the aerodynamic performance as well as the flow stability in the desired flight state. The RAE2822 airfoil is chosen as the initial airfoil. A benchmark of the unsteady aerodynamic configuration optimization design considering buffet suppression is developed. First, the numerical methods are verified and the damping rate of disturbance is chosen as a constraint in the aerodynamic optimization to extend the buffet onset. Then, the surrogate models constructed by the radial basis function interpolation are used to replace the computational fluid dynamics (CFD) solver. The teaching- and learning-based optimization (TLBO) is used. Finally, the aerodynamic and the flow stability characteristics of the airfoil before and after optimization are compared and analyzed. The proposed optimization framework can not only improve the aerodynamic characteristics in the cruise state but can also suppress the transonic buffet on higher angles of attack.

The friction performance and compression properties of geotextile bags under different degrees of consolidation are researched through the slope sliding test, direct shear test, and unconfined compression test in this study. The geotextile bags are made up of geotextile and tailings sands obtained from a construction site of a prototype tailings dam in Yunnan Province. The slope sliding test is considered as an easy method to study the friction performance of geotextile bags with different degrees of consolidation. Through the test, the friction coefficients between the bags were obtained. Given the geotextile bags can withstand the vertical load in practical engineering, the direct shear test is also proposed and conducted. The ultimate bearing capacity of the geotextile bags with different consolidation degrees is studied in the unconfined compression test. The test reveals that the ultimate bearing capacity of geotextile bags, although featured with different moisture contents before the test, stays the same under the condition of slow loading. Finally, a stability analysis method based on the limit equilibrium theory is developed to simulate the stability of the tailings dam using geotextile bags (TDGB). According to the test results, the TDGB has demonstrated an improved stability compared with the general tailings dam. [ABSTRACT FROM AUTHOR]

Two or more consumer species compete for a same source in a competitive model, The amount of a limiting resource in the environment reduces when two or more species compete for it, These species also confront other threats for their survival, such as health concerns, infection, pollution, and so on, Based on above, in this paper we develop a competition model where we have consider two logistically growing species competing for the same resource, Also, there is infection in one of the species, We study the influence of disease and pollutants on the competing population with delay in the transmission of infection in infective class, The characteristics of the model has been discussed to prove that the described system is bounded, The existence of infection-free equilibrium point and endemic equilibrium point of the system has been shown, in case of coexistence of the species, The stability analysis of the equilibrium points has been examined using the Routh-Hui twiz criteria, The occurrence of hopf bifurcation considering time lag (15) as a critical parameter has been examined, The direction and stability of hopf bifurcation has been investigated, Numerical simulations have been performed using MATLAB to prove our analytical results. [ABSTRACT FROM AUTHOR]

In this work, a numerical framework for global stability analysis of rigid-body-motion fluid–structure-interaction problems is presented. The Jacobian matrices which arise in the linearization procedure are derived numerically via the first-order finite difference scheme. The linearized fluid–structure coupled equations are solved using an immersed boundary method. The linear stability solver is first tested on two canonical cases, i.e., the flow past a stationary cylinder and the flow past an isolated elastically mounted cylinder. An excellent agreement between the results obtained here and those from available published research is achieved. The solver is then used to study the linear stability of the flow past two elastically mounted cylinders in tandem arrangement. The variations in growth rate and frequency of two leading modes with reduced velocity are examined. The mechanisms of lock-in and galloping phenomena observed in nonlinear simulation are elucidated from the perspective of linear instabilities in the leading modes. [ABSTRACT FROM AUTHOR]

Huanglongbing (HLB) is a plant disease mainly spread by the insect-borne citrus psyllid. It is the most destructive citrus pathosystem worldwide. To understand the impact of sexual transmission on HLB dynamics, we propose a host–vector–HLB compartment model incorporating two transmission routes. The basic reproduction number ℛ 0 is derived. Various interventions of the disease are assessed. We also investigate the effect of different incidence functions to simulate sexual transmission. For the case of sublinear incidence functions, the disease-free equilibrium is globally asymptotically stable (GAS) provided ℛ 0 < 1. For mass action incidence of sexual transmission, the endemic equilibrium is GAS provided ℛ 0 > 1. However, under nonlinear incidence, it is proved that the model may exhibit backward bifurcation. Theoretical and numerical studies reveal that (i) different forces of infection between heterosexual psyllids in the model may have a distinct impact on disease dynamics; (ii) sensitivity analysis shows that for ℛ 0 , the transmission rate between host and vector is more sensitive parameter than that between heterosexual psyllids; (iii) if the sexual transmission is ignored, the disease burden is likely to be underestimated in comparison with realistic scenarios; (iv) in the absence of chemical insecticides, the combined use of yellow sticky traps and injection of nutrient solutions can be more effective in suppressing the spread of HLB. These findings provide valuable insights for public policymakers to determine the long-term viability of implemented HLB management strategies and highlight the urgency of finding sustainable HLB solutions. [ABSTRACT FROM AUTHOR]

This article analyzes the global stability of synchronous reference frame phase-locked loops (SRF-PLLs) from a large signal viewpoint. First, a large-signal model of SRF-PLL is accurately established, without applying any linearization method. Then, according to the phase portrait and Lyapunov argument, the global performance of SRF-PLL is discussed in the nonlinear frame. Compared with the small-signal analysis methods, the proposed analysis, not relying on the small-signal model and linearization method, provides a global discussion of the SRF-PLL performance. The contributions of this article are as follows. First, it is found that SRF-PLL has infinite equilibrium points, including stable points and saddle points. Second, it provides a way to divide the global region of SRF-PLL into many small regions. In each small region, the SRF-PLL only has one stable equilibrium point. And for any initial states $(\tilde{\theta }(t_0),\tilde{\omega }(t_0))$ in a small region, all states $(\tilde{\theta }(t),\tilde{\omega }(t)),t>t_0$ will remain in this small region, and SRF-PLL will converge to the unique stable equilibrium point of this small region. Third, by dividing the global region of SRF-PLL into many small regions, it is found that when the frequency of grids varies largely, the SRF-PLL will converge to a new equilibrium point that is far away from the original equilibrium point. It is the reason why the frequency convergence of SRF-PLL has many oscillations and SRF-PLL has a rather slow dynamic, when the frequency changes largely. The experimental results are provided to verify the proposed global stability analysis of SRF-PLL. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle's stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis. [ABSTRACT FROM AUTHOR]

We analyse epidemic model in this article, with incubation delay under the effect of pollution, where disease transmission follows saturated incidence rate and quadratic treatment has also been considered. Boundedness and presence of endemic equilibrium point (Q) as well as point of infection-free equilibrium (Q*) for the model has been established. We investigate the stability analysis of the model around Q and Q*. R0 as a basicreproduction number has been calculated. When R0 < 1, the model is stable for Q, but when R0 > 1, it shifts from a stable to an unstable environment for ϱ > 0. Using center manifold theory, it was shown that at R0 = 1, the model exhibits backward bifurcation, when the bifurcating constant a > 0, while if a < 0, then the bifurcation is forward. We analyse the presence of Hopf bifurcation for endemic equilibrium point Q* by taking time delay as the critical parameter. Considering the normal form theory, we obtain the direction and the stability of Hopf Bifurcation. We establish the global stability of Q* using Lyapunov Lasalle theorem. Our results indicate that pollution affects the disease transmission dynamics of the model. We observe that in the diseased model with pollution the survival of the species is significantly less as compared when there is only disease and no pollution. Numerical simulations are performed to validate our logical findings. [ABSTRACT FROM AUTHOR]

Climate variability affects the changes in controlling diseases transferred by insects. An increase in the population, the growth of communities, and a lack of public health infrastructure bring about the return of diseases of which insects are carriers, one of the illness issues. Therefore, the disease control is significant to help reduce the burden on the government and strengthen the country's public health structure. This research proposes a novel approach to modeling dengue fever dynamics, we employ a fractional derivative model with the Atangana–Baleanu–Caputo derivative, which offers a more accurate representation of real-world disease dynamics compared to traditional integer-order models. Basic qualifications are proposed. Equilibrium points and basic reproduction numbers are analyzed. The next-generation matrix method is used to identify the transmission. Besides, parameter sensitivity analysis is performed to learn about factors affecting input parameter values' effects on the basic reproduction number. It was found that the most common parameter affecting the transmission was the biting rate of mosquitoes was 1. In addition, the existence and uniqueness of the solution are examined using the Banach fixed point theorem. The Toufik–Atangana method is used for the numerical examination of a fractional version of the proposed model. We compared different values of fractional-order α=0.965, 0.975, 0.985, 0.995 and 1 it was found that when the order of derivatives decreases, the transmission shall decrease accordingly. This research provides valuable insights for developing effective control strategies to reduce the burden of dengue fever and strengthen public health systems. [ABSTRACT FROM AUTHOR]

• Methodology of Global Stability Analysis and its post-processing are presented. • Methodology provides curves of the amplification-factor envelope. • Direct prediction of laminar-turbulent position shift induced by steps demonstrated. • All trends observed in the experiments are captured by proposed methodology. Reliable prediction of the effect of surface irregularities on laminar-turbulent transition (LTT) is of great importance for many industrial applications. At low levels of free-stream turbulence typical of external aerodynamics, the primary mechanism of LTT is associated with the so-called convective instability of the Tollmien-Schlichting waves. In this paper, a non-empiric methodology based on Global Stability Analysis, which has been developed and validated previously to predict the evolution of these waves and the location of the LTT on a smooth flat plate, is applied to evaluation of this effect for backward- and forward- facing steps of different heights and locations. The results obtained are analyzed and compared with results of 2D time-accurate unsteady Navier-Stokes simulations, as well as with available experimental data and with the semi-empiric "variable N -factor" method. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a mathematical model of cancer including tumor cells, immune cells, and normal cells is investigated when a delay term is induced. Though the model was originally proposed by De Pillis et al. (Math. Comput. Model. 37:1221–1244, 2003), to make the model more realistic, we have added a delay term into the model, and it has incorporated novelty in our present work. The stability of existing equilibrium points in the delay-induced system is studied in detail. Global stability conditions of the tumor-free equilibrium point have been found. It is shown that due to this delay effect, the coexisting equilibrium point may lose its stability through a Hopf bifurcation. The implicit function theorem is applied to characterize a complex function in a neighborhood of delay terms. Additionally, the presence of Hopf bifurcation is demonstrated when the transversality conditions are satisfied. The length of delay for which the solutions preserve the stability of the limit cycle is estimated. Finally, through a series of numerical simulations, the theoretical results are formally examined. [ABSTRACT FROM AUTHOR]

Copyright of Rad HAZU: Matematicke Znanosti is the property of Croatian Academy of Sciences & Arts (HAZU) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we consider a system of second order rational difference equations. We mainly discuss the boundedness and persistence, existence of fixed point, and uniqueness of positive fixed point, local and global behavior of positive fixed point and rate of convergence of every positive solution of the system under discussion. It will be shown that the system under discussion exhibits some special dynamics such as same mathematical condition for existence of fixed point and its global stability. Finally, some numerical examples are provided for verification of theoretical results.

abstract: Current practices in structural engineering demand ever-increasing knowledge and expertise concerning stability of structures from professionals in this field. This paper implements standardized procedures for geometrically nonlinear analysis of steel and reinforced concrete structures, with the objective of comparing methodologies with one another and with a geometrically exact finite element analysis performed with Ansys 14.0. The following methods are presented in this research: Load Amplification Method, from NBR 8800:2008; the γ z coefficient method, from NBR 6118:2014; the P-Delta iterative method and the α c r coefficient method, prescribed in EN 1993-1-1:2005. A bibliographic review focused on standardized approximate methods and models for consideration of material and geometric nonlinearities is presented. Numerical examples are included, from which information is gathered to ensure a valid comparison between methodologies. In summary, the presented methods show a good correlation of results when applied within their respective recommended applicability limits, of which, Eurocode 3 seems to present the major applicability range. The treated approximate methods show to be more suitable for regular framed structures subjected to regular load distributions.

The SARS-CoV-2 continues to spread across the world. During this COVID-19 pandemic, several variants of the SARS-CoV-2 have been found. Some of these new variants like the VOC-202012/01 of lineage B.1.1.7 or the most recently B.1.617 emerging in India have a higher infectiousness than those previously prevalent. We propose a mathematical model based on ordinary differential equations to investigate potential consequences of the appearance of a new more transmissible SARS-CoV-2 strain in a given region. The proposed mathematical model incorporates the presymptomatic and asymptomatic subpopulations in addition to the more usual susceptible, exposed, infected, and recovered subpopulations. This is important from a realistic point of view since it has been found recently that presymptomatic and asymptomatic individuals are relevant spreaders of the SARS-CoV-2. Using the next-generation matrix method, we find the basic reproduction number, R 0 , an important threshold parameter that provides insight regarding the evolution and outcome of a certain instance of the COVID-19 pandemic. The local and global stability of system equilibria are also presented. In particular, for the global stability we construct a Lyapunov functional and use the LaSalle invariant principle to prove that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. On the other hand, if R 0 > 1 the endemic equilibrium is globally asymptotically stable. Finally, we present numerical simulations to numerically support the analytic results and to show the impact of the introduction of a new more contagious SARS-CoV-2 variant in a population. [ABSTRACT FROM AUTHOR]

In this article, we study the non-standard finite difference (NSFD) schemes for the diabetes mellitus with tuberculosis infection. We have classified diabetes mellitus into two categories such as diabetes without complications and with complications and studied diabetes with tuberculosis infection. We have modelled diabetes with tuberculosis infection with linear and nonlinear model and studied the local and global asymptotic stability analysis using the NSFD scheme.

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle’s stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis.

Q fever (query fever) is classified as one of the likely zoonosis that is transmissible to humans from farm animals. The disease may lead to significant economic losses to livestock owners. The deterministic dynamics of direct transmission, different shedding rates, treatment, the effect of relapse, and seasonality of disease remains an open problem. Therefore, this study introduces direct transmission cycle, different shedding rates, treatment, the effect of relapse, and time-dependent parameters. We obtain control reproduction expressions for the model under different scenarios. Using Lyapunov functions, we establish that the non-seasonal model is globally asymptotically stable. The extension of the model to include seasonal trends shows that there exists a positive periodic solution. The global sensitivity method used shows that imperfect treatment reduces the rate of indirect transmission, but, leads to an increase in direct transmission by symptomatic cattle herds. Optimal control model is also utilized to explore the impact of time-dependent treatment, disinfectant, and separate facilities for animal birthing. We show the control efficacies; and also calculated the average cost-effectiveness ratio, and the incremental cost-effectiveness ratio. We hope that this study further enlightens farm owners on the use of other interventions in controlling Q fever disease in livestock.

Estimates of rape against women had been usually taken from two main sources till the early 1980s; The national crime victimization study and the Uniform Crime Report’s official statistics. Scholars argued, however, that the true incidence of rape was greatly underestimated by those data sources. For example, a uniform crime report focuses on recorded incidents, but several violations are not reported to the police. Two methodological causes have contributed to the underestimation of rape by national crime surveys. First, its definition of rape was considered too limited because it covered only carnal information and, thus, omitted many actions, such as offenses other than penile-vaginal penetration, from the scope of contemporary rape laws. Second, critics argued that the national crime survey was inappropriately structured for interviewees who had previously been assaulted to generate allegations of abuse. The crux of this critique was that there was no clear concern about rape in the national crime survey. How to establish evaluation methods that would show the real nature of rape was the crucial question. As a result of this, we are inspired to design a new mathematical model in this paper to study the dynamics of rape in our societies. Several characteristics of the established model, such as model formulation, boundedness, equilibrium solutions, basic reproduction number, global stability analysis are derived. The existence and characterization of the optimal control function are carried out. For sensitivity analysis as well as to show the significance of the control strategies, several simulation results are given. To get a deep insight into the dynamical behavior of the model, numerical simulations are performed and consequently we obtain the graphical results based on parameters taken as variables. The Euler technique is employed to do the job.

Middle East Respiratory Syndrome Coronavirus (MERS-CoV) can cause mild to severe acute respiratory illness with a high mortality rate. As of January 2020, more than 2500 cases of MERS-CoV resulting in around 860 deaths were reported globally. In the absence of neither effective treatment nor a ready-to-use vaccine, control measures can be derived from mathematical models of disease epidemiology. In this manuscript, we propose and analyze a compartmental model of zoonotic MERS-CoV transmission with two co-circulating strains. The human population is considered with eight compartments while the zoonotic camel population consist of two compartments. The expression of basic reproduction numbers are obtained for both single strain and two strain version of the proposed model. We show that the disease-free equilibrium of the system with single stain is globally asymptotically stable under some parametric conditions. We also demonstrate that both models undergo backward bifurcation phenomenon, which in turn indicates that only keeping R 0 below unity may not ensure eradication. To the best of the authors knowledge, backward bifurcation was not shown in a MERS-CoV transmission model previously. Further, we perform normalized sensitivity analysis of important model parameters with respect to basic reproduction number of the proposed model. Furthermore, we perform optimal control analysis on different combination interventions with four components namely preventive measures such as use of masks, isolation of strain-1 infected people, strain-2 infected people and infected camels. Optimal control analysis suggests that combination of preventive measures and isolation of infected camels will eventually eradicate the disease from the community. [ABSTRACT FROM AUTHOR]

The essential objective of this research article is to investigate stability issue of neutral-type Cohen–Grossberg neural networks involving multiple time delays in states of neurons and multiple neutral delays in time derivatives of states of neurons in the network. By exploiting a modified and improved version of a previously introduced Lyapunov functional, a new sufficient stability criterion is obtained for global asymptotic stability of Cohen–Grossberg neural networks of neutral-type possessing multiple delays. The proposed new stability condition does not involve the time and neutral delay parameters. The obtained stability criterion is totally dependent on the system elements of Cohen–Grossberg neural network model. Moreover, the validity of this novel global asymptotic stability condition may be tested by only checking simple appropriate algebraic equations established within the parameters of the considered neutral-type neural network. In addition, an instructive numerical example is presented to indicate the advantages of our proposed stability result over the existing literature results obtained for stability of various classes of neutral-type neural networks having multiple delays. [ABSTRACT FROM AUTHOR]

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 0 1 and the strain 2 reproduction number R 0 2 . 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. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of a vector-borne disease model with two transmission paths: direct transmission through contact and indirect transmission through vector. The direct transmission is considered to be a nonmonotone incidence function to describe the psychological effect of some severe diseases among the population when the number of infected hosts is large and/or the disease possesses high case fatality rate. The system has a disease-free equilibrium which is locally asymptotically stable when the basic reproduction number ( R 0 ) is less than unity and may have up to four endemic equilibria. Analytical expression representing the epidemic growth rate is obtained for the system. Sensitivity of the two transmission pathways were compared with respect to the epidemic growth rate. We numerically find that the direct transmission coefficient is more sensitive than the indirect transmission coefficient with respect to R 0 and the epidemic growth rate. Local stability of endemic equilibrium is studied. Further, the global asymptotic stability of the endemic equilibrium is proved using Li and Muldowney geometric approach. The explicit condition for which the system undergoes backward bifurcation is obtained. The basic model also exhibits the hysteresis phenomenon which implies diseases will persist even when R 0 < 1 although the system undergoes a forward bifurcation and this phenomenon is rarely observed in disease models. Consequently, our analysis suggests that the diseases with multiple transmission routes exhibit bistable dynamics. However, efficient application of temporary control in bistable regions will curb the disease to lower endemicity. Additionally, numerical simulations reveal that the equilibrium level of infected hosts decreases as psychological effect increases. [ABSTRACT FROM AUTHOR]

A numerical framework of global stability analysis based on the immersed boundary (IB) method is established for predicting the unsteadiness onset of flow system including complex geometry. The solid wall is considered as the boundary force term and the stability analysis is applied on the orthogonal Cartesian grid, which facilitate the application of spectral collocation method in the stability analysis. To convert the linearized N-S equation with source term to homogeneous, the boundary force can be viewed as an unknown quantity, and then the no-slip boundary condition is introduced into the governing equation to close the system. The method is first tested on two canonical cases, the flow past a stationary cylinder and an isolated airfoil. The relevant results are consistent with phenomena observed in the numerical calculations and experiments, verifying the effectiveness of the method. Applying the spectral collocation method contributes to the accuracy of stability analysis and reduces the grid nodes, making it more feasible to consider complex geometry. Then, to highlight the superiority of treating the flow system with complex geometry, such as including multi-objects, the method is applied to the stability analysis of the flow past a four-square-arranged cylinder cascade. The abundant instability perturbation modes induced by the interaction of multi-objects and the corresponding relationship with the whole system are captured, which is also verified by the unsteady calculation. [ABSTRACT FROM AUTHOR]

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

The stable operation and control of the proposed terrestrial multi-terminal Voltage Source Converter (VSC) medium voltage DC (MVDC) distribution network is a remarkable motivation towards developing the future universal DC grid interconnecting the low voltage DC systems on one side and the high voltage DC systems on the other. The small-signal stability analysis are important in designing these power electronic based systems (PEBS). In this study, small-signal stability approaches for PEBS are reviewed with the aim of identifying suitable methods for the proposed MVDC distribution network. It is established that the impedance-based methods are suitable for local stability analysis complementing very well with the state-space modelling-eigenvalue analysis method best for global stability analysis. The Lyapunov linearisation method offers simple, adaptable, and accurate small-signal and large-signal stability study. On the other hand, the bifurcation analysis is an emerging non-linear approach with promising efficiency and precision. In conclusion, there is no single small-signal stability criterion that encompass an acceptable level of accuracy, adaptability, and efficiency. Thus, the impedance-based methods combined with state-space modelling-eigenvalue analysis, Lyapunov linearisation, and bifurcation theory can be suitable small-signal stability approaches for the multi-terminal MVDC distribution network.

The viral infection of hepatitis B virus (HBV) is a dangerous problem for health around the globe and counted in the top leading causes of death. To explore the viral dynamics of this infection, an HBV epidemic model has been developed by dividing the infected compartment into three subclasses, acute, chronically infected and carrier individuals with both vertical as well as horizontal transmission. After formulating the model, we prove that the positive solution of the model exists. The next generation matrix approach has been used to investigate the threshold quantity known as basic reproduction number. The global stability conditions at endemic equilibria (EE) and disease-free equilibrium (DFE) are established by using the method of geometrical approach and Castillo-Chavez, respectively. We use the optimization theory and the three time-dependent control variables to establish the control program. By the help of this control policy, we reduce the number of susceptible, acute, chronically hepatitis B infected and carrier persons, while the numbers of recovered and vaccinated populations are maximized. Finally, numerical results will be found out for the support and feasibility of the analytical results. [ABSTRACT FROM AUTHOR]

This work performs a numerical investigation on the two-dimensional flow across two circular cylinders in staggered arrangement at Re = 100. The seaparting distances between the centers of the cylinders are D / d = 4–10 with Δ D / d = 2 and T / d = 0.0–2.0 with Δ T / d = 0.5 in the streamwise and transverse directions, respectively, in which d is the cylinder diameter. Although the low- Re flow across staggered cylinders has been studied in a number of works, the authors mainly concerned about the identification and transition of various flow patterns. In this work, our objective is to quantitatively reveal the characteristics of flow unsteadiness as affected by the two separating distances. The flow unsteadiness is assessed from several aspects, including the spatial distributions and temporal variations of instantaneous flow patterns, fluctuating characteristic quantities, and fluctuating flow in the gap and in the near- and far-wake regions. To investigate the inherent instability of the flow, the global linear stability and sensitivity analysis is further carried out to demonstrate the unstable mode of perturbation growth and the critical flow patterns that destabilize the flow. The numerical results reveal that the wake flow between the two centerlines and beside the upstream cylinder is the most intensely perturbed. The flow around the downstream cylinder exhibits great fluctuation as perturbed by the destabilized shear layer of the upstream cylinder. The flow downstream of both cylinders shows multiple peak fluctuation of velocity because of the complex interactions between the destabilized shear layer and the wake vortices, resulting in the bidirectional transverse propagation of fluctuation. The stability analysis demonstrates that the unstable mode of perturbation growth is more significant in the far-wake region as the two cylinders are placed in proximity; the sensitivity analysis shows that the gap flow is crucial for the flow destabilization at small D, while the wake flow of cylinder- B is more significant for large D. [ABSTRACT FROM AUTHOR]

The stable operation and control of the proposed terrestrial multi-terminal Voltage Source Converter (VSC) medium voltage DC (MVDC) distribution network is a remarkable motivation towards developing the future universal DC grid interconnecting the low voltage DC systems on one side and the high voltage DC systems on the other. The small-signal stability analysis are important in designing these power electronic based systems (PEBS). In this study, small-signal stability approaches for PEBS are reviewed with the aim of identifying suitable methods for the proposed MVDC distribution network. It is established that the impedance-based methods are suitable for local stability analysis complementing very well with the state-space modelling-eigenvalue analysis method best for global stability analysis. The Lyapunov linearisation method offers simple, adaptable, and accurate small-signal and large-signal stability study. On the other hand, the bifurcation analysis is an emerging non-linear approach with promising efficiency and precision. In conclusion, there is no single small-signal stability criterion that encompass an acceptable level of accuracy, adaptability, and efficiency. Thus, the impedance-based methods combined with state-space modelling-eigenvalue analysis, Lyapunov linearisation, and bifurcation theory can be suitable small-signal stability approaches for the multi-terminal MVDC distribution network. [ABSTRACT FROM AUTHOR]

In this article, we study the non-standard finite difference (NSFD) schemes for the diabetes mellitus with tuberculosis infection. We have classified diabetes mellitus into two categories such as diabetes without complications and with complications and studied diabetes with tuberculosis infection. We have modelled diabetes with tuberculosis infection with linear and nonlinear model and studied the local and global asymptotic stability analysis using the NSFD scheme. [ABSTRACT FROM AUTHOR]