Invariance Principle Research Articles

Unifying Procedure-Dependent Preference Reversals: Theory and Experiments

Revealed preferences between alternatives can be systematically reversed across a variety of elicitation procedures (e.g., choice, valuation, matching, joint/separate evaluation). These puzzling findings have been usually invoked to challenge the procedure invariance principle. Yet procedure-dependent preferences can be endogenous. This paper presents a unifying theory of contextual deliberation to account for seemingly disparate phenomena of preference reversals. When attribute importance is ex ante imperfectly known, people can engage in costly information retrieval/acquisition activities (i.e., deliberation) prior to making decisions. Elicitation procedures can influence revealed preferences through affecting the incentive for deliberation. Therefore, contextual deliberation can endogenously yield procedure-dependent preference reversals, offer a common microfoundation for extant psychological accounts (e.g., the prominence hypothesis, the evaluability hypothesis), and coherently organize apparently unrelated/inconsistent findings in the literature. We also run five experiments and document new findings that are inconsistent with extant hypotheses but can be reconciled by contextual deliberation. This paper was accepted by Dmitri Kuksov, marketing. Funding: This work was supported by the Hong Kong Research Grant Council (RGC) General Research Fund [Grant 16500614]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2021.02640 .

Scheduling in the High-Uncertainty Heavy Traffic Regime

We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual diffusion scale as opposed to asymptotically vanishing disturbances studied previously in relation to heavy traffic. A main advantage of the approach is that the invariance principle underlying diffusion limits makes it possible to define uncertainty classes in terms of the first two moments only. The model we consider is a single-server queue with multiple job types. The problem is formulated as a zero sum stochastic game played between the system controller, who determines scheduling and attempts to minimize an expected linear holding cost, and an adversary, who dynamically controls the service time distributions of arriving jobs and attempts to maximize the cost. The heavy traffic asymptotics of the game are fully solved. It is shown that an asymptotically optimal policy for the system controller is to prioritize according to an index rule, and for the adversary, it is to select distributions based on the system’s current workload. The workload-to-distribution feedback mapping is determined by a Hamilton–Jacobi–Bellman equation, which also characterizes the game’s limit value. Unlike in the vast majority of results in the heavy traffic theory and as a direct consequence of the diffusive size disturbances, the limiting dynamics under asymptotically optimal play are captured by a stochastic differential equation where both the drift and the diffusion coefficients may be discontinuous. Funding: R. Atar is supported by the Israeli Science Foundation [Grant 1035/20].

Invariance Principles for Nonlinear Discrete-Time Switched Systems and Its Application to Output Synchronization of Dynamical Networks.

In this article, we develop two invariance principles for nonlinear discrete-time switched systems based on multiple Lyapunov functions and multiple weak Lyapunov functions, respectively, which allow the first differences of multiple weak Lyapunov functions to be positive on certain sets. It is shown that the solution of the system is attracted to the largest weakly invariant set in a certain specific region. Then, based on the invariance principle developed and geometrical dissipativity, we obtain the generalized output synchronization for discrete-time dynamical networks with nonidentical nodes by an appropriate switching among several communication topologies. Finally, two examples are provided to demonstrate the effectiveness of the main results.

Development of stigma scale for women with mental illness in perinatal period, validity and reliability study

AimAlthough there are many scales that measure stigma, there is no scale with the necessary adequacy to measure stigma in the perinatal period. The study aims to develop the stigma scale for women with mental illness in the perinatal period and test its validity and reliability.Materials and methodsParticipants were reached via patients, visitors, and hospital staff who applied to Sakarya Training and Research Hospital between 01/06/2022 and 01/12/2022. Two hundred people (female n = 134, male n = 66) aged 18–65 participated in the study and "Sociodemographic data form," "Perinatal Mental Illness Stigma Scale (PMISS)," "Social Distance Scale," and "Beliefs Towards Mental Illness Scale" were used to collect data. Data were analyzed using SPSS 22 and the AMOS 26 program.ResultsThe Content Validity Index of the scale items was between 0.80–1. Cronbach's alpha coefficient score of the general scale was 0.94, the "Discrimination and Prejudice" sub-dimension was 0.93, and the "Labeling" sub-dimension was 0.88. It was determined that item-total score correlations varied between 0.410 and 0.799. P value calculated < 0.05 in Barlett's test and 0.94 in the Kaiser-Meyer Olkin test. These values show that factor analysis can be applied to the scale. According to the Exploratory Factor Analysis result, the scale has a 2-factor structure, explaining 60% of the total variance. The Guttman Split-Half coefficient of the scale was 0.882, and the Spearman-Brown coefficient was 0.883. The scale was reapplied to 30 participants with an interval of three weeks. The correlation coefficient between the two measurements was 0.91, indicating that the scale satisfies the invariance principle over time.ConclusionThe PMISS is a reliable measurement tool that can be used to investigate stigma towards mental illness during the perinatal period in the Turkish population.

Mathematical Modelling and Numerical Simulation of Hepatitis B Viral Infection: The Case of Burkina Faso

Hepatitis is a viral infection that can cause inflammation of the liver and lead to severe liver damage and even death. The study of hepatitis in Burkina Faso is crucial for several reasons. Indeed, understanding the epidemiology of hepatitis in Burkina Faso can help develop effective prevention and control strategies, and its study can contribute to a better understanding of the global burden of the disease and the development of effective interventions in other parts of the world. To this aim, a new differential susceptibility and infectivity mathematical model of Hepatitis B transmission was developed in order to simulate the potential spread of the Hepatitis B virus in the population of Burkina Faso. Once the mathematical model is presented, the existence and uniqueness of non-negative solutions are proved. The model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R01 and a globally asymptotically stable endemic equilibrium when R0 &gt; 1. The global asymptotic stability of the disease-free equilibrium has been studied using the Castillo Chavez method [5]. The Lyapunov function and the LaSalle invariance principle are used to prove the global asymptotic stability of the endemic equilibrium [26, 4, 18]. To simulate the proposed model, a Matlab numerical code has been developed. Numerical simulations are performed using data of Burkina Faso. The obtained numerical results confirm analytical results as well as the evolution of hepatitis B in Burkina Faso.

Brownian Particle in the Curl of 2-D Stochastic Heat Equations

We study the long time behaviour of a Brownian particle evolving in a dynamic random environment. Recently, Cannizzaro et al. (Ann Probab 50(6):2475–2498, 2022) proved sharp log\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\log }$$\\end{document}-super diffusive bounds for a Brownian particle in the curl of (a regularisation of) the 2-D Gaussian Free Field (GFF) ω̲\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\underline{\\omega }$$\\end{document}. We consider a one parameter family of Markovian and Gaussian dynamic environments which are reversible with respect to the law of ω̲\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\underline{\\omega }$$\\end{document}. Adapting their method, we show that if s≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s\\ge 1$$\\end{document}, with s=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s=1$$\\end{document} corresponding to the standard stochastic heat equation, then the particle stays log\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\log }$$\\end{document}-super diffusive, whereas if s<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s<1$$\\end{document}, corresponding to a fractional heat equation, then the particle becomes diffusive. In fact, for s<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s<1$$\\end{document}, we show that this is a particular case of Komorowski and Olla (J Funct Anal 197(1):179–211, 2003), which yields an invariance principle through a Sector Condition result. Our main results agree with the Alder–Wainwright scaling argument (see Alder and Wainwright in Phys Rev Lett 18:988–990, 1967; Alder and Wainwright in Phys Rev A 1:18–21, 1970; Alder et al. in Phys Rev A 4:233–237, 1971; Forster et al. in Phys Rev A 16:732–749, 1977) used originally in Tóth and Valkó (J Stat Phys 147(1):113–131, 2012) to predict the log\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log $$\\end{document}-corrections to diffusivity. We also provide examples which display loga\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log ^a$$\\end{document}-super diffusive behaviour for a∈(0,1/2]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a\\in (0,1/2]$$\\end{document}.

Global Stability of a Delayed Model for the Interaction of SARS-CoV-2/ACE2 and Adaptive Immunity

The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the culprit behind the coronavirus disease 2019 (COVID-19), which has killed millions of people. SARS-CoV-2 binds its spike (S) protein to the angiotensin-converting enzyme 2 (ACE2) receptor to inter the epithelial cells in the respiratory tracts. ACE2 is a crucial mediator in the SARS-CoV-2 infection pathway. In this paper, we construct a mathematical model to describe the SARS-CoV-2/ACE2 interaction and the adaptive immunological response. The model predicts the effects of latently infected cells as well as immunological responses from cytotoxic T lymphocytes (CTLs) and antibodies. The model is incorporated with three distributed time delays: (i) delay in the formation of latently infected epithelial cells, (ii) delay in the activation of latently infected epithelial cells, (iii) delay in the maturation of new released SARS-CoV-2 virions. We show that the model is well-posed and it admits five equilibria. The stability and existence of the equilibria are precisely controlled by four threshold parameters Ri, i=0,1,2,3. By formulating suitable Lyapunov functions and applying LaSalle's invariance principle, we show the global asymptotic stability for all equilibria. To demonstrate the theoretical results, we conduct numerical simulations. We do sensitivity analysis and identify the most sensitive parameters. We look at how the latent phase, ACE2 receptors, antibody and CTL responses, time delays affect the dynamical behavior of SARS-CoV-2. Although the basic reproduction number R0 is unaffected by the parameters of antibody and CTL responses, it is shown that viral replication can be hampered by immunological activation of antibody and CTL responses. Further, our findings indicate that R0 is affected by the rates at which the ACE2 receptor grows and degrades. This could provide valuable guidance for the development of receptor-targeted vaccines and medications. Furthermore, it is shown that, increasing time delays can effectively decrease R0 and then inhibit the SARS-CoV-2 replication. Finally, we show that, excluding the latently infected cells in the model would result in an overestimation of R0.

Generalized Invariance Principles for Stochastic Dynamical Systems and Their Applications

Investigating long-term behaviors of stochastic dynamical systems often requires to establish criteria that are able to describe delicate dynamics of the considered systems. In this article, we develop generalized invariance principles for continuous-time stochastic dynamical systems. Particularly, in a sense of probability one and by the developed semimartingale convergence theorem, we not only establish a local invariance principle, but also provide a generalized global invariance principle that allows the sign of the diffusion operator to be positive in some bounded region. We further provide an estimation for the time when a trajectory, initiating outside a particular bounded set, eventually enters it. Finally, we use several representative examples, including stochastic oscillating dynamics, to illustrate the practical usefulness of our analytical criteria in deciphering the stabilization or/and the synchronization dynamics of stochastic systems.

THE VARIETY OF INVARIANCE IN FORMAL AND REGIONAL ONTOLOGIES

The paper examines the invariance principles proposed by the analytical and phenomenological traditions for demarcating the boundaries of formal and regional ontologies. The principle of invariance with respect to isomorphic transformations, generalizing Alfred Tarski’s criterion for logical concepts, is extended to formal ontology as the theory of manifolds in its phenomenological interpretation. Isomorphism types, which are abstract individuals of the highest order, hypostases of forms of all possible ontologies, are considered as model-theoretical analogs of manifolds. The correlativity of the phenomenological principles of demarcation of ontological regions and the criterion of invariance with respect to isomorphic transformations is demonstrated, leading to the convergence of logic and formal mathematics in both traditions and, at the same time, to the exclusion of geometry from formal ontology. Particular attention is paid to the discussion of the analytical and phenomenological traditions of the synthetic (material) a priori and the contribution that Wittgenstein’s doctrine on internal relations at different stages of its evolution makes to this discussion. The paper reveals the basis for later Wittgenstein’s criticism of his earlier project of creating a phenomenological language for expressing internal regional relations (such as the colours exclusion). The paper shows how Wittgenstein’s doubts about the possibility of an ideal notation based on the dichotomy of the logical and phenomenological led him to the study of invariants arising in language games. These invariants are not determined by the special properties of the categorical objects of formal ontology or the structures of regional subject matter, but are stable equilibria generated by the “consensus of actions.” New perspectives are outlined that are opened for logic and phenomenology by switching focus from the invariants of ontological structures to the invariants of structured interactions of various agents.

Deterministic Gradient-Descent Learning of Linear Regressions: Adaptive Algorithms, Convergence Analysis and Noise Compensation.

Weight learning forms a basis for the machine learning and numerous algorithms have been adopted up to date. Most of the algorithms were either developed in the stochastic framework or aimed at minimization of loss or regret functions. Asymptotic convergence of weight learning, vital for good output prediction, was seldom guaranteed for online applications. Since linear regression is the most fundamental component in machine learning, we focus on this model in this paper. Aiming at online applications, a deterministic analysis method is developed based on LaSalle's invariance principle. Convergence conditions are derived for both the first-order and the second-order learning algorithms, without resorting to any stochastic argument. Moreover, the deterministic approach makes it easy to analyze the noise influence. Specifically, adaptive hyperparameters are derived in this framework and their tuning rules disclosed for the compensation of measurement noise. Comparison with four most popular algorithms validates that this approach has a higher learning capability and is quite promising in enhancing the weight learning performance.

Global properties of delayed models for SARS-CoV-2 infection mediated by ACE2 receptor with humoral immunity

&lt;abstract&gt;&lt;p&gt;The coronavirus disease 2019 (COVID-19) is caused by a new coronavirus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). SARS-CoV-2 infects the epithelial (target) cells by binding its spike protein, S, to the angiotensin-converting enzyme 2 (ACE2) receptor on the surface of epithelial cells. During the process of SARS-CoV-2 infection, ACE2 plays an important mediating role. In this work, we develop two models which describe the within-host dynamics of SARS-CoV-2 under the effect of humoral immunity, and considering the role of the ACE2 receptor. We consider two discrete (or distributed) delays: (ⅰ) Delay in the SARS-CoV-2 infection of epithelial cells, and (ⅱ) delay in the maturation of recently released SARS-CoV-2 virions. Five populations are considered in the models: Uninfected epithelial cells, infected cells, SARS-CoV-2 particles, ACE2 receptors and antibodies. We first address the fundamental characteristics of the delayed systems, then find all possible equilibria. On the basis of two threshold parameters, namely the basic reproduction number, $ \Re_{0} $, and humoral immunity activation number, $ \Re_{1} $, we prove the existence and stability of the equilibria. We establish the global asymptotic stability for all equilibria by constructing suitable Lyapunov functions and using LaSalle's invariance principle. To illustrate the theoretical results, we perform numerical simulations. We perform sensitivity analysis and identify the most sensitive parameters. The respective influences of humoral immunity, time delays and ACE2 receptors on the SARS-CoV-2 dynamics are discussed. It is shown that strong stimulation of humoral immunity may prevent the progression of COVID-19. It is also found that increasing time delays can effectively decrease $ \Re_{0} $ and then inhibit the SARS-CoV-2 replication. Moreover, it is shown that $ \Re_{0} $ is affected by the proliferation and degradation rates of ACE2 receptors, and this may provide worthy input for the development of possible receptor-targeted vaccines and drugs. Our findings may thus be helpful for developing new drugs, as well as for comprehending the dynamics of SARS-CoV-2 infection inside the host.&lt;/p&gt;&lt;/abstract&gt;

Global co-dynamics of viral infections with saturated incidence

&lt;abstract&gt;&lt;p&gt;Several mathematical models of two competing viruses (or viral strains) that have been published in the literature assume that the infection rate is determined by bilinear incidence. These models do not show co-existence equilibrium; moreover, they might not be applicable in situations where the virus concentration is high. In this paper, we developed a mathematical model for the co-dynamics of two competing viruses with saturated incidence. The model included the latently infected cells and three types of time delays: discrete (or distributed): (ⅰ) The formation time of latently infected cells; (ⅱ) The activation time of latently infected cells; (ⅲ) The maturation time of newly released virions. We established the mathematical well-posedness and biological acceptability of the model by examining the boundedness and nonnegativity of the solutions. Four equilibrium points were identified, and their stability was examined. Through the application of Lyapunov's approach and LaSalle's invariance principle, we demonstrated the global stability of equilibria. The impact of saturation incidence, latently infected cells, and time delay on the viral co-dynamics was examined. We demonstrated that the saturation could result in persistent viral coinfections. We established conditions under which these types of viruses could coexist. The coexistence conditions were formulated in terms of saturation constants. These findings offered new perspectives on the circumstances under which coexisting viruses (or strains) could live in stable viral populations. It was shown that adding the class of latently infected cells and time delay to the coinfection model reduced the basic reproduction number for each virus type. Therefore, fewer treatment efficacies would be needed to keep the system at the infection-free equilibrium and remove the viral coinfection from the body when utilizing a model with latently infected cells and time delay. To demonstrate the associated mathematical outcomes, numerical simulations were conducted for the model with discrete delays.&lt;/p&gt;&lt;/abstract&gt;

Mathematical Modeling of COVID‐19 Disease Dynamics With Contact Tracing: A Case Study in Ethiopia

In this paper, we developed a mathematical model for the dynamics of coronavirus disease (COVID‐19) transmission. The model embraces the notion of contact tracing and contaminated surfaces which are vital for disease control and contribute to disease transmission, respectively. We analyzed the model properties such as the positivity of the solution, invariant region, existence, and stability nature of equilibria. Besides, we computed the basic reproduction number R0. The local stability and the global stability of disease‐free equilibrium (DFE) points are proved by using the Routh–Hurwitz criteria and the Castillo‐Chavez and Song approach, respectively. LaSalle’s invariant principle is applied to prove the stability of an endemic equilibrium (EE) point. The possibility of bifurcation is discussed using the center manifold theory. We used real data on the spread and control of COVID‐19 disease in Ethiopia. Based on the data reported, we estimated the values of the parameters using the least squares method together with the fmin function in the MATLAB optimization toolbox. The sensitivity analysis of the model is explored numerically to illustrate the impact of the parameters on disease transmission. The study addressed that contact tracing is especially important because COVID‐19 often has asymptomatic carriers, and there are many asymptomatic individuals unaware in Ethiopia. The new infections would decrease in the communities by detecting and isolating COVID‐19 cases before they could spread the virus to others. Moreover, the study endorsed that the contaminated surface has contributed to disease transmission. The sensitivity analysis shows that if the rate of disinfected contaminated objects (ϕ) rises, then the transmission of the disease is reduced. Consequently, this study will aid in the fight against COVID‐19 policymakers and NGOs. It can also be used as a policy input for different countries under this crisis. Because of the mathematical modeling of this global pandemic, there is another point of view rather than public health research outputs. Additionally, with the concept of contact tracing and contaminated surfaces incorporated into the model, the result provides insight for disease prevention.

A Novel Low-Winding-Loss Circulated Interleaving Structure for Planar Transformers Based on Current Invariance Principle

A Novel Low-Winding-Loss Circulated Interleaving Structure for Planar Transformers Based on Current Invariance Principle

From quenched invariance principle to semigroup convergence with applications to exclusion processes

From quenched invariance principle to semigroup convergence with applications to exclusion processes

Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence

&lt;abstract&gt;&lt;p&gt;This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results.&lt;/p&gt;&lt;/abstract&gt;

Global dynamics of a delayed model with cytokine-enhanced viral infection and cell-to-cell transmission

&lt;abstract&gt;&lt;p&gt;Recent studies have demonstrated the superiority of cell-to-cell transmission over cell-free virus infection, and highlighted the role of inflammatory cytokines in enhancing viral infection. To investigate their impacts on viral infection dynamics, we have proposed an HIV infection model incorporating general incidence rates, these infection modes, and two time delays. We derived the basic reproduction number and showed that it governs the existence and local stability of steady states. Through the construction of appropriate Lyapunov functionals and application of the LaSalle invariance principle, we established the global asymptotic stability of both the infection-free and infected steady states.&lt;/p&gt;&lt;/abstract&gt;

Periodic Behaviour of HIV Dynamics with Three Infection Routes

In this study, we consider a system of nonlinear differential equations modeling the human immunodeficiency virus type-1 (HIV-1) in a variable environment. Infected cells were subdivided into two compartments describing both latently and productively infected cells. Thus, three routes of infection were considered including the HIV-to-cell contact, latently infected cell-to-cell contact, and actively infected cell-to-cell contact. The nonnegativity and boundedness of the trajectories of the dynamics were proved. The basic reproduction number was determined through an integral operator. The global stability of steady states is then analyzed using the Lyapunov theory together with LaSalle’s invariance principle for the case of a fixed environment. Similarly, for the case of a variable environment, we showed that the virus-free periodic solution is globally asymptotically stable once R0≤1, while the virus will persist once R0&gt;1. Finally, some numerical examples are provided illustrating the theoretical investigations.

Mathematical analysis of in-host Ebola virus infection dynamics model with sensitivity analysis

Ebola virus (EBOV) causes a haemorrhagic and lethal Ebola disease disastrous to human beings, which is transmitted by contact of body fluids of infected animals and humans. Presently, there are no therapies for the disease. In this paper, a mathematical model is proposed to investigate the in-vivo dynamics of EBOV infection with sensitivity analysis. A system of five non-linear ordinary differential equations constitutes the model, from which the basic reproduction number, R0 is calculated using the next generation matrix method. The parameter R0 is employed to analyze global stability of disease-free and endemic equilibria. Using the Metzler matrix operator, the results indicate that the disease-free equilibrium point is globally asymptotically stable provided that R0 &lt; 1, which implies that the disease disappears from the host after some period of time. With Lyapunov Stability Theory and LaSalle Invariant Principle, the results indicate that the endemic equilibrium point is globally asymptotically stable provided that R0 &gt; 1, which implies that the disease persists in the host. Sensitivity analysis of the basic reproduction number pertaining to the model parameters is achieved using forward normalized sensitivity index method. The results indicate that the parameters for infection rate, production rate of uninfected target cells and virus replication rate are positively sensitive. On the other hand, the parameters for natural death rate of target cells and natural death rate of the virus are negatively sensitive, implying that the basic reproduction number decreases as the parameters increase and vice versa. Besides, it is shown that the parameter for the infection rate is the most sensitive one while the parameter for the virus reproduction rate is the least sensitive one. Numerical simulations are used to validate the analytical results. The results suggest implementation of deliberate control measures to eradicate EBOV disease by considering sites in the model to which the most sensitive parameters are affiliated.

On the distinction between corpuscular and wave processes and the arbitrariness in the basis of special relativity theory

This article is devoted to the criticism of the wave-particle dualism and the provisions of the special theory of relativity (SRT). The fallacy of accepting the extended principle of relativity and identifying particles and waves is shown. The substantiation is given that the own fields of physical objects, which are material substances and spatially connect physical objects with each other, are the medium of propagation of light waves. The causal and visual picture of the propagation of light waves is considered, and the features of the mechanism of their propagation in comparison with other types of waves are described. On the basis of an alternative method for obtaining the relativistic law of velocities addition, the inconsistency of the principle of invariance of the interval adopted in the framework of SRT is shown. The inconsistency of the SRT positions and conclusions regarding the so-called relativistic effects—time dilation, mass increase, length decrease, as well as the energy of relativistic particles is shown. The presence of the clock paradox is shown by a simple example. The conclusion is made about the incorrectness of using mathematical transformations of Lorentz and the four-dimensional continuum in the physical representation.