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Abstract: Abstract In this study, we first introduce a SIV in-host model of virus transmission with linear infection rate. Further, the model is enhanced by adding nonlinear infection rate and logistic growth to account for more realistic approach to the modeling of viral transmission. Note that, the nonlinear infection rate is assumed to be a Holling type II kind function, similar to Beddington-DeAngelis functional response. The primary motivation is to analyze and compare the dynamical behavior of the cells and virus population during viral transmission for both the models. The qualitative stability analysis is carried out for the equilibrium states of the two models and it has been found that the virus free equilibrium (VFE) state (for both the models) is locally stable when basic reproduction number (BRN) is less than unity and unstable otherwise. Further, a unique endemic equilibrium (EE) state is obtained when BRN is greater than unity for the model with linear infection rate. Whereas, for the second model, a unique EE state exists under some parametric conditions. The stability criterion of the EE state is stated using Routh-Hurwitz criterion. In the case of the model with nonlinear infection rate, backward bifurcation occurs when the equilibrium value of target cells exceeds a specific constant threshold when BRN is equal to unity. To validate the qualitative findings, extensive numerical simulations are performed which provide significant biological insights. Different scenarios are considered for the numerical simulation and it has been found that all variables exhibit a periodic nature in the presence of logistic growth and linear infection rate. To observe the impact of certain parameters of interest, we perform the sensitivity analysis on both the both models. The findings suggest that the sensitivity of the infection rate ( \(\beta\) ) has contrasting effects on the two models. Specifically, in the first model, as \(\beta\) increases, the number of infected cells increases, whereas in the second model, the number of infected cells decreases with increasing values of \(\beta\) . Moreover, the first model ensures the clinical fact that the virus will wash out of the bloodstream of the host. PubDate: 2024-08-27
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Abstract: Abstract In this work, only two independent conditions for the oscillation of all solutions of even-order delay differential equations in the non-canonical case are established. Using comparison techniques with first- and second-order delay differential equations, we obtain easy-to-apply criteria that improve previous results in the literature. In addition, we show the importance of our results by applying them to examples that have been frequently used in related works. PubDate: 2024-08-21
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Abstract: Abstract This article proposes an analytical model for suspension bridges with the vibrating cables in frame of coupled systems of fractional-order boundary value problems. The proposed model includes particular multi-point boundary conditions describing interrelationship between the main body of the bridge and suspending cables. The governing problems of this analytical model are indeed coupled nonlinear differential equations of different fractional orders. The main aim of this investigation is to solve the model making use of the fixed point theory and the, stabilize it. Solvability process of this analytical model is given separately according to the resonance and non-resonance cases arising from boundary conditions. Making use of the Green function technique included in a fixed point problem, a novel uniqueness criterion is proposed to guarantee the solvability of the fractional-order model under investigation in the non-resonance case. Besides, in order to find the same solvability criteria in the resonance case, the coincidence degree theory is chosen. Next, we have a stability analysis in the sense of Mittag-Leffler for the vibrating cables of the bridge. The practical efficiency of the theoretical findings is supported by numerical prototypes. PubDate: 2024-08-10
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Abstract: Abstract In this paper, we are concerned with the following periodic damped vibration system $$\begin{aligned} \ddot{u}+q(t){\dot{u}}-L(t)u+\nabla W(t,u)=0. \end{aligned}$$ Using variational methods and a version of the concentration compactness principle, we study the existence of ground state homoclinic solutions for this system under two different classes of superquadratic conditions weaker than the ones known in the literature. To the best of our knowledge, there has been no work focused in this case. PubDate: 2024-07-18
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Abstract: Abstract We investigate the long-term smooth evolution of a semilinear Lamé system within bounded regions of \(\mathbb {R}^3\) , subject to Dirichlet boundary conditions and nonlinear forces of critical nature. The challenge lies in addressing the fact that the semigroups exhibit singular behavior as \(\varepsilon \) approaches 0. This parameter \(\varepsilon \) appears in the second-order time derivative of the displacement vector, introducing complexities into the model. Our focus is on understanding the dynamics of solutions as \(\varepsilon \rightarrow 0^+\) . Results regarding the well-posedness of the systems, quasi-stability, existence, finite dimensionality, regularity, and the robustness of attractors are proven. PubDate: 2024-07-06
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Abstract: Abstract Cooperation during hunting is one of the generic strategies adopted by the predators that creates fear among their prey. In this study, an eco-epidemiological model is proposed by incorporating the cost of fear that significantly impacts prey reproduction and the rate of disease transmission. The existence and local stability of all biologically feasible equilibrium points of the model are presented. Effects of various important factors viz., hunting cooperation, predation rate, disease transmission rate and prey reproduction rate on the system dynamics are explored. Codimension one and codimension two bifurcations, including Chenciner and Fold-Neimark Sacker bifurcation, are obtained. Homoclinic orbits initiating from a Bogdanov-Takens bifurcation point are observed. Furthermore, a catastrophic shift is observed while varying the death rate of infected prey and a bistability region for the same parameter is obtained. Finally, mortality and disease induced positive Hydra effect are observed in the proposed model. PubDate: 2024-07-03
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Abstract: Abstract In this paper we classify the phase portraits in the Poincaré disc of a class of cubic polynomial differential systems having an invariant ellipse and an invariant straight line. We prove that such a class of cubic polynomial differential systems have exactly 43 topologically different phase portraits in the Poincaré disc. Also we obtain that the invariant ellipse in two of these phase portraits is a limit cycle. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00597-9
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Abstract: Abstract Consider the first order differential system given by $$\begin{aligned} \begin{array}{l} {\dot{x}}= y, \qquad {\dot{y}}= -x+a(1-y^{2n})y, \end{array} \end{aligned}$$ where a is a real parameter and the dots denote derivatives with respect to the time t. Such system is known as the generalized Rayleigh system and it appears, for instance, in the modeling of diabetic chemical processes through a constant area duct, where the effect of adding or rejecting heat is considered. In this paper we characterize the global dynamics of this generalized Rayleigh system. In particular we prove the existence of a unique limit cycle when the parameter \(a\ne 0\) . PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00604-z
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Abstract: Abstract Condition spectrum is an essential generalization of the spectrum. This article considers the condition spectrum of bounded linear operators on Banach space and develops certain topological properties. It is observed that the condition spectrum is useful than the spectrum and pseudospectrum for identifying the norm behavior of non-normal matrices. For a bounded linear operator A on a Banach space, we find upper and lower bounds for \(\Vert e^{tA}\Vert , \, t\ge 0\) and \(\Vert A^n\Vert ,\, n=1,2,\ldots\) using the condition spectrum of A. These bounds are used to identify the transient effect of the quantities appearing in the time dependent linear dynamical system. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00623-w
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Abstract: Abstract This paper is concerned with time global behavior of solutions to nonlinear Schrödinger equation with a non-vanishing condition at the spatial infinity. Under a non-vanishing condition, it would be expected that the behavior is determined by the shape of the nonlinear term around the non-vanishing state. To observe this phenomenon, we introduce a generalized version of the Gross-Pitaevskii equation, which is a typical equation involving a non-vanishing condition, by modifying the shape of nonlinearity around the non-vanishing state. It turns out that, if the nonlinearity decays fast as a solution approaches to the non-vanishing state, then the equation admits a global solution which scatters to the non-vanishing element for both time directions. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00609-8
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Abstract: Abstract In our earlier work [J. R. Singler, Math. Methods Appl. Sci. 40 (2017), no. 8, 2896–2906], we studied the existence of a global attractor for a low order ODE system with a possibly indefinite linear term and a non-quadratic nonlinearity that either conserves energy or yields a weak energy decrease. The ODE system with the energy-conserving nonlinearity has been used many times as a model problem to attempt to gain new understanding of transition to turbulence in viscous incompressible fluid flows. The ODE system with the weak energy-decreasing nonlinearity can also be seen as a model problem for a viscous incompressible fluid flow with a nonlinear outflow boundary condition. We used a nonstandard energy function in our earlier work to provide new conditions on the problem matrices guaranteeing the existence of a global attractor. In this note we improve our earlier results in two ways. First, we extend our results to hold for a much wider class of scalar functions in the nonlinear term. Second, we obtain sharper results for the case when the nonlinear term causes a weak energy decrease. We illustrate our new results with examples. Our results provide new examples of low order ODE systems that can be explored to obtain new insight concerning the interactions of an indefinite linear term with an energy-conserving or weak energy-decreasing nonlinearity. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00590-2
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Abstract: Abstract In this article, a spatial epidemic model with media coverage is studied. By both mathematical analysis and numerical simulation, we found that there are some typical dynamics of population density such as the formation of the hole, stripe, spot, coexistence of hole and stripe or spot and stripe. The obtained results exhibit that parameters describing media coverage have a significant influence on the spatial pattern of the disease. More specifically, the sequential change in behaviour of the spatial pattern is observed as the parameter that accounts for media coverage increases. These changes analogous to the effect due to the rise in the basic reproduction number. The results presented in this article thus can be applied to any particular disease with some modification to study the effects of media coverage on disease dynamics. The model is although simple but the idea can be well extended to other complex problems. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00595-x
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Abstract: Abstract COVID-19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modeling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection. From the stability analysis of the equilibrium points, it was found that the infection-free equilibrium point remains locally asymptotically stable when \(R_0 < 1\) , and when \(R_0\) is greater than one, the infected equilibrium point remains locally asymptotically stable. The results of the optimal control study show that infection decreases with the implementation of an optimal treatment strategy, and that a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00593-z
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Abstract: In this paper, we consider a class of fractional order semilinear abstract Cauchy problem with state dependent delay subject to nonlocal initial conditions, and enlarge the existence theory with two different sets of assumptions. Under the first set of assumptions, we establish the existence of Hölder classical solution. Since the Hölder exponent appears as an exponent on the metric function in contraction inequality, it is not suitable to use Banach contraction mapping principle. Krasnoselskii’s fixed point theorem becomes effective to overcome this situation. Under the second set of assumptions, we obtain only the existence of mild solution using Schauder’s fixed point theorem. Few examples have been provided to illustrate our results. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00600-3
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Abstract: Abstract In this paper, the problems of positivity and exponential stability a BAM-Cohen-Grossberg neural networks model with time-varying delays and nonlinear self-excitation rates are studied. By novel comparison techniques via differential-integral inequalities, the exponential convergence of state trajectories to a unique positive equilibrium is established by tractable linear programming conditions, which can be effectively solved by various convex optimization algorithms. Numerical simulations are given to illustrate the effectiveness of the obtained theoretical results. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00605-y
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Abstract: In this paper, the existence of positive periodic solutions of neural networks with time-varying delays is discussed by using the fixed point theory on cones. Some necessary and sufficient conditions guaranteeing the existence of one positive periodic solution of the considered system are established. Finally, we exhibit an example to verify the applicability of our abstract results. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00591-1
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Abstract: Abstract Sustainable forest management is one of the warming issues in the present century. In this manuscript, we have employed the model of control theory to control the consequence of toxicity and illegal logging of mature trees in the ecosystem of Sundarbans, the largest mangrove forest in the world. In this investigation, we have momentarily mentioned some of the fields in which these challenges are present. These fields especially consist of sustainable forestry management of ecosystem. We have reflected on the modified Leslie-Gower response function to set up as the alternative resource for industries when forestry resources are divested. The boundedness, persistence, equilibria and stability are examined.Our main aim is to investigate the spans and applications of control theory to control the effect of toxicity and illegal logging. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00589-9
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Abstract: Abstract In this paper we consider autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter \(\varepsilon\) goes to zero. We present some remarks on asymptotic behavior of the global attractors which lead us to conclude the lower semicontinuity of this attractors at \(\varepsilon\) equal to zero. We also prove the finite-dimensionality of the attractors. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00610-1
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Abstract: Abstract The purpose of this work is the study of the qualitative behavior of the homogeneous in space solution of a delay differential equation arising from a model of infection dynamics. This study is mainly based on the monotone dynamical systems theory. Existence and smoothness of solutions are proved, and conditions of asymptotic stability of equilibriums in the sense of monotone dynamical systems are formulated. Then, sufficient conditions of global stability of the nonzero steady state are derived, for the two typical forms of the function f, specifying the efficiency of immune response-mediated virus elimination. Numerical simulations illustrate the analytical results. The obtained theoretical results have been applied, in a context of COVID-19 data calibration, to forecast the immunological behaviour of a real patient. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00594-y
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Abstract: Abstract In this work, we study the monotonicity of the ratio of two line integrals $$\begin{aligned} I_{i}(h)=\int _{\Gamma _{h}^{+}}f_{i}(x)ydx+\int _{\Gamma _{h}^{-}}f_{i}(x)ydx, i=0,1, \end{aligned}$$ with \(\Gamma ^{+}_{h}=\lbrace (x,y)\in {\mathbb {R}}^{2}~\vert ~ H^{+}(x,y)=h,~x> 0\rbrace\) and \(\Gamma _{h}^{-}=\lbrace (x,y)\in {\mathbb {R}}^{2}~\vert ~ H^{-}(x,y)={\tilde{h}},~x\le 0\rbrace\) , where \(H^{+}(x,y)\) and \(H^{-}(x,y)\) have the form \(\frac{1}{2}y^{2}+\Psi _{1}(x)\) and \(\frac{1}{2}y^{2}+\Psi _{2}(x)\) , respectively. We first present a criterion function defined directly by the functions which appear in the above integrals and prove the monotonicity of this criterion function implying the monotonicity of the ratio of these line integrals which is very important to find the number of limit cycles. Then we give several examples to illustrate the application of this criterion. PubDate: 2024-07-01 DOI: 10.1007/s12591-022-00599-7
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