Showing papers in "Ricerche Di Matematica in 2020"

Effects of information-dependent vaccination behavior on coronavirus outbreak: insights from a SIRI model

Abstract: A mathematical model is proposed to assess the effects of a vaccine on the time evolution of a coronavirus outbreak. The model has the basic structure of SIRI compartments (susceptible–infectious–recovered–infectious) and is implemented by taking into account of the behavioral changes of individuals in response to the available information on the status of the disease in the community. We found that the cumulative incidence may be significantly reduced when the information coverage is high enough and/or the information delay is short, especially when the reinfection rate is high enough to sustain the presence of the disease in the community. This analysis is inspired by the ongoing outbreak of a respiratory illness caused by the novel coronavirus COVID-19.

General alternative regularization method for solving split equality common fixed point problem for quasi-pseudocontractive mappings in Hilbert spaces

Abstract: We propose a general alternative regularization algorithm for solving the split equality fixed point problem for the class of quasi-pseudocontractive mappings in Hilbert spaces. We also illustrate the performance of our algorithm with numerical example and compare the result with some other algorithms in the literature in this direction. We found out that our algorithm requires a lesser number of iterations and CPU time for its convergence than some of the existing algorithms. Our results extend and generalize some existing results in the literature in this direction.

A generalized Gompertz growth model with applications and related birth-death processes

Abstract: In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

Impact of farming awareness based roguing, insecticide spraying and optimal control on the dynamics of mosaic disease

Abstract: Control interventions and farming knowledge are equally important for plant disease control. In this article, a mathematical model has been derived using saturated response functions (nonlinear infection rate) for studying the dynamics of mosaic disease with farming awareness based roguing (removal of infected plants) and insecticide spraying . It is assumed that the use of roguing and spraying depend on the level of awareness about the disease. The model possesses three equilibria namely the trivial, which is always unstable, the disease-free equilibrium which is stable if the basic reproduction number is below unity and the coexisting which may be stable or can exhibit Hopf-bifurcation under certain condition. Finally, we have opted an optimal control problem introducing three control parameters for determining the optimal level of roguing, spraying and cost regarding media awareness for cost-effective control of mosaic disease. Numerical simulations establish the main results suggesting that the awareness campaigns through radio, TV advertisement are important for eradication of the disease. Also, awareness campaign, roguing and spraying should be incorporated with optimal level for cost effective control of mosaic disease.

Analysis of a plankton–fish model with external toxicity and nonlinear harvesting

Abstract: In this paper, we consider a three species plankton–fish system that incorporates external toxicity and nonlinear harvesting. We consider that the growth of species are affected directly or indirectly by an external toxic substance and the feeding of the predator on the affected prey is considered as Holling type II functional response. All the possible biological feasible equilibrium points are determined analytically as well as numerically and performed stability analysis around these equilibrium points. It is shown that the system undergoes for Hopf bifurcation when the growth rate of prey passes some threshold value. Furthermore, Pontryagin’s maximum principle has been applied to obtain optimal control of harvesting to maximize the benefit as well as the conservation of the ecosystem. We perform numerical simulations to justify and illustrate our analytical results. Some numerical tools such as phase portraits, time evaluation and bifurcation diagrams are presented to ensure the complex dynamics in the system. Period doubling cascade route to chaos is examined and validated through the numerical calculation of Lyapunov exponents and sensitivity analysis.

Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

Abstract: In this paper, we develop a new disease-resistant mathematical model with a fraction of the susceptible class under imperfect vaccine and treatment of both the symptomatic and quarantine classes. With standard incidence when the associated reproduction threshold is less than unity, the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium. It is then proved that this phenomenon vanishes either when the vaccine is assumed to be 100% potent and perfect or the Standard Incidence is replaced with a Mass Action Incidence in the model development. Furthermore, the model has a unique endemic and disease-free equilibria. Using a suitable Lyapunov function, the endemic equilibrium and disease free equilibrium are proved to be globally-asymptotically stable depending on whether the control reproduction number is less or greater than unity. Some numerical simulations are presented to validate the analytic results.

Control of mosaic disease using microbial biostimulants: insights from mathematical modelling

Abstract: A major challenge to successful crop production comes from viral diseases of plants that cause significant crop losses, threatening global food security and the livelihoods of countries that rely on those crops for their staple foods or source of income. One example of such diseases is a mosaic disease of plants, which is caused by begomoviruses and is spread to plants by whitefly. In order to mitigate negative impact of mosaic disease, several different strategies have been employed over the years, including roguing/replanting of plants, as well as using pesticides, which have recently been shown to be potentially dangerous to the environment and humans. In this paper we derive and analyse a mathematical model for control of mosaic disease using natural microbial biostimulants that, besides improving plant growth, protect plants against infection through a mechanism of RNA interference. By analysing the stability of the system’s steady states, we will show how properties of biostimulants affect disease dynamics, and in particular, how they determine whether the mosaic disease is eradicated or is rather maintained at some steady level. We will also present the results of numerical simulations that illustrate the behaviour of the model in different dynamical regimes, and discuss biological implications of theoretical results for the practical purpose of control of mosaic disease.

Approximation of common solution of finite family of monotone inclusion and fixed point problems for demicontractive multivalued mappings in CAT(0) spaces

Abstract: In this paper, we use the gate condition on two multivalued k-demicontractive mappings to approximate a common solution of a finite family of monotone inclusion problem and fixed point problem in CAT(0) space. Furthermore, we propose a Halpern-type proximal point algorithm and prove its strong convergence to a common solution of a finite family of monotone inclusion problems and fixed point problem for two multivalued k-demicontractive mappings in a complete CAT(0) space. We also applied our result to the problem of finding a common solution of a finite family of minimization problem and fixed point problem in CAT(0) space. Finally, numerical experiments of our result are presented to further show its applicability.

Oblique derivative problems and Feller semigroups with discontinuous coefficients

Abstract: This paper is devoted to the functional analytic approach to the problem of existence of Markov processes with an oblique derivative boundary condition for second-order, uniformly elliptic differential operators with discontinuous coefficients. More precisely, we construct Feller semigroups associated with absorption, reflection, drift and sticking (or viscosity) phenomena at the boundary. The approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the Calderon–Zygmund theory of singular integral operators with non-smooth kernels.

Similarity solutions for strong shock waves in magnetogasdynamics under a gravitational field

Abstract: In the present paper, we use a Lie group of transformations to obtain a class of similarity solutions to a problem of cylindrically symmetric strong shock waves propagating through one-dimensional, unsteady, and isothermal flow of a self-gravitating ideal gas under the influence of azimuthal magnetic field. The density of the ambient medium is assumed to be non-uniform ahead of the shock. The generators of the Lie group of transformations involve arbitrary constants which yield four different cases of possible solutions. Out of all possibilities, only two cases hold similarity solutions. One is with a power law shock path, and the other one is with an exponential law shock path. We present a detailed investigation for the case of power law shock path. Numerical computations have been performed to find out the flow patterns in the flow-field behind the shock. Also, we have analyzed the effects of variation in adiabatic index, ambient density exponent, gravitational parameter, and Alfven-Mach number on the flow variables behind the shock. All computations have been done using the software package MATLAB.

Modelling competitive interactions and plant–soil feedback in vegetation dynamics

Abstract: Plant–soil feedback is recognized as a causal mechanism for the emergence of vegetation patterns of the same species especially when water is not a limiting resource (e.g. humid environments) (Carteni et al. in J Theor Biol 313:153–161, 2012. https://doi.org/10.1016/j.jtbi.2012.08.008 ; Marasco et al. in Bull Math Biol 76(11):2866–2883, 2014. https://doi.org/10.1007/s11538-014-0036-6 ). Nevertheless, in the field, plants rarely grow in monoculture but compete with other plant species. In these cases, plant–soil feedback was shown to play a key role in plant-species coexistence (Mazzoleni et al. in Ecol Model 221(23):2784–2792, 2010. https://doi.org/10.1016/j.ecolmodel.2010.08.007 ). Using a mathematical model consisting of four PDEs, we investigate mechanisms of inter- and intra-specific plant–soil feedback on the coexistence of two competing plant species. In particular, the model takes into account both negative and positive feedback influencing the growth of the same and the other plant species. Both the coexistence of the plant species and the dominance of a particular plant species is examined with respect to all model parameters together with the emergence of spatio-temporal vegetation patterns.

Subspace code constructions

Abstract: We improve on the lower bound of the maximum number of planes of $$\mathrm{PG}(8,q)$$ mutually intersecting in at most one point leading to the following lower bound: $$\mathcal A_q(9, 4; 3) \ge q^{12}+2q^8+2q^7+q^6+q^5+q^4+1$$. We also construct two new non–equivalent $$(6, (q^3-1)(q^2+q+1), 4; 3)_q$$–constant dimension subspace orbit–codes.

An extension of weighted generalized cumulative past measure of information

Abstract: In this paper, we consider a shift-dependent measure of generalized cumulative entropy and its dynamic (past) version in the case where the weight is a general non-negative function. Our results include linear transformations, stochastic ordering, bounds and aging classes properties and some relationships with other survival concepts. We also define the conditional weighted generalized cumulative entropy and weighted generalized cumulative Kerridge inaccuracy measure. For these concepts, we obtain some properties and characterization results under suitable assumptions. Finally, we propose an estimator of this shift-dependent measure using empirical approach. In addition, we study large sample properties of this estimator.

Approximation of eigenvalues of evolution operators for linear coupled renewal and retarded functional differential equations

Abstract: Recently, systems of coupled renewal and retarded functional differential equations have begun to play a central role in complex and realistic models of population dynamics. In view of studying the local asymptotic stability of equilibria and (mainly) periodic solutions, we propose a pseudospectral collocation method to approximate the eigenvalues of the evolution operators of linear coupled equations, providing rigorous error and convergence analyses and numerical tests. The method combines the ideas of the analogous techniques developed separately for renewal equations and for retarded functional differential equations. Coupling them is not trivial, due to the different state spaces of the two classes of equations, as well as to their different regularization properties.

Fixed point results for new type of multivalued mappings in bounded metric spaces with an application

Abstract: In this paper, we prove some fixed point results for multivalued mappings in bounded metric spaces via symmetric spaces. Moreover an application to an integral inclusion is given.

Converging strong shock waves in magnetogasdynamics under isothermal condition

Abstract: The similarity solutions to the problem of cylindrically symmetric strong shock waves in an ideal gas with a constant azimuthal magnetic field are presented. The flow behind the shock wave is assumed to spatially isothermal rather than adiabatic. We use the method of Lie group invariance to determine the possible class of self-similar solutions. Infinitesimal generators of Lie group transformations are determined by using the invariance surface conditions to the system and on the basis of arbitrary constants occurring in the expressions for the generators, four different possible cases of the solutions are reckoned and we observed that only two out of all possibilities hold self-similar solutions, one of which follows the power law and another follows the exponential law. To obtain the similarity exponents numerical calculations have been performed and comparison is made with the existing results in the literature. The flow patterns behind the shock are analyzed graphically.

Global dynamics of a diffusive viral infection model with general incidence function and distributed delays

Abstract: The distributed delay was firstly proposed by Volterra in the 1930s since it is more realistic than discrete delay and has been introduced in many dynamical systems. In this paper, we establish a diffusive viral infection model with general incidence function and distributed delays subject to the homogeneous Neumann boundary conditions. Firstly, we prove the existence, uniqueness, positivity and boundedness of solutions of the model. Then, by using the linearization method and constructing appropriate Lyapunov functionals, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection $$\mathcal {R}_{0}$$ , which implies that the global stability of the model precludes the existence of complex dynamical behaviors such as Hopf bifurcation and patter formation. Furthermore, an example is presented and numerical simulations are also carried out to illustrate the main results.

On the signless Laplacian and normalized Laplacian spectrum of the zero divisor graphs

Abstract: Let R be a commutative ring with nonzero identity and let $$\Gamma (R)$$ denote the zero divisor graph of R. In this paper, we describe the signless Laplacian and normalized Laplacian spectrum of the zero divisor graph $$\Gamma (\mathbb {Z}_n)$$, and we determine these spectrums for some values of n. We also characterize the cases that 0 is a signless Laplacian eigenvalue of $$\Gamma (\mathbb {Z}_n)$$. Moreover, we find some bounds for some eigenvalues of the signless Laplacian and normalized Laplacian matrices of $$\Gamma (\mathbb {Z}_n)$$.

Lack of exponential decay for a thermoelastic laminated beam under Cattaneo’s law of heat conduction

Abstract: Feng (Complexity, Art 5139419, 2020) studied a thermoelastic laminated Timoshenko beam, where the heat conduction is given by Cattaneo’s law, as well as established the exponential and polynomial stabilities depending on the stability number $$\chi _\tau $$ In this short paper, we consider the same system and show a lack of exponential stability when the stability number $$\chi _\tau e 0$$ , by using Gearhart–Herbst–Pruss–Huang theorem

Riemann solutions to the logotropic system with a Coulomb-type friction

Abstract: The motivation of this study is to analyze the structure of the Riemann solutions for compressible hyperbolic system, so called logotropic system, with a Coulomb-type friction. The classical wave solutions of the Riemann problem (RP) for the logotropic system are structured explicitly for all cases. The system considered in this problem is hyperbolic in nature and the characteristic fields associated with the characteristics are genuinely nonlinear. It is shown that the Riemann solutions for the logotropic system with a Coulomb-type friction term composed of the rarefaction wave and shock wave. It is found that the Coulomb-type friction term, appearing in the governing equations, influences the Riemann solution for the logotropic system.

Entropy solutions of anisotropic elliptic nonlinear obstacle problem with measure data

Abstract: We prove the existence of an entropy solution for a class of nonlinear anisotropic elliptic unilateral problem associated to the following equation $$\begin{aligned} -\sum _{i=1}^{N} \partial _i a_i(x,u, abla u) -\sum _{i=1}^{N}\partial _{i}\phi _{i}( u)=\mu , \end{aligned}$$where the right hand side $$\mu $$ belongs to $$L^{1}(\Omega )+ W^{-1, \vec {p'}}(\Omega )$$. The operator $$-\sum _{i=1}^{N} \partial _i a_i(x,u, abla u) $$ is a Leray–Lions anisotropic operator and $$\phi _{i} \in C^{0}({\mathbb {R}}, {\mathbb {R}})$$.

On almost revlex ideals with Hilbert function of complete intersections

Abstract: In this paper, we investigate the behavior of almost reverse lexicographic ideals with the Hilbert function of a complete intersection. More precisely, over a field K, we give a new constructive proof of the existence of the almost revlex ideal $$J\subset K[x_1,\ldots ,x_n]$$ , with the same Hilbert function as a complete intersection defined by n forms of degrees $$d_1\le \cdots \le d_n$$ . Properties of the reduction numbers for an almost revlex ideal have an important role in our inductive and constructive proof, which is different from the more general construction given by Pardue in 2010. We also detect several cases in which an almost revlex ideal having the same Hilbert function as a complete intersection corresponds to a singular point in a Hilbert scheme. This second result is the outcome of a more general study of lower bounds for the dimension of the tangent space to a Hilbert scheme at stable ideals, in terms of the number of minimal generators.

Parallel coordinates in three dimensions and sharp spectral isoperimetric inequalities

Abstract: In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes et al. (Adv Calc Var 10:357–380, 2017) that “the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area” under the weaker restriction that the boundary of the domain is diffeomorphic to the sphere and convex or axiconvex. We also provide partial results in arbitrary dimensions.

Existence and uniqueness results in weighted spaces for Dirichlet problem in unbounded domains

Abstract: We study the Dirichlet problem for a second order linear elliptic partial differential equation with discontinuous coefficients in unbounded domains. We establish an existence and uniqueness result.

Comparing chains in a Banach space

Abstract: We prove that in a Banach space with the metric approximation property the flat chains defined by De Pauw and Hardt (Am J Math 134:1–69, 2012) coincide with those of Adams (J Geom Anal 18:1–28, 2008).

Helmholtz-type solitary wave solutions in nonlinear elastodynamics

Abstract: The propagation of localised (in space-time) waves is analysed in the context of the dynamic theory of incompressible hyperelastic solids subject to body forces corresponding to a dual power-law substrate potential. A broad class of exact solutions is obtained which, under the assumption of slow modulation, incorporates Helmholtz-type solitary waves. The linear stability of these solutions is studied under the assumption that the speed of propagation of the wave is small enough compared to the speed at which transverse waves travel in the linear regime and in the absence of external actions.

A safe harbor can protect an endangered species from its predators

Abstract: The objective is the study of the dynamics of a prey–predator model where the prey species can migrate between two patches. The specialist predator is confined to the first patch, where it consumes the prey following the simple law of mass action. The prey is further “endangered” in that it suffers from the strong Allee effect, assumed to occur due to the lowering of successful matings. In the second patch the prey grows logistically. The model is formulated in a comprehensive way so as to include specialist as well as generalist predators, as a continuum of possible behaviors. This model described by a set of three ordinary differential equation is an extension of some previous models proposed and analysed in the literature on metapopulation models. The following analysis issues will be addressed: boundedness of the solution, equilibrium feasibility and stability, and dynamic behaviour dependency of the population and environmental parameters. Three types for both equilibria and limit cycles are possible: trivial, predator-free and coexistence. Classical analysis techniques are used and also theoretical and numerical bifurcation analysis. Besides the well-known local bifurcations, also a homoclinic connection as a global bifurcation is calculated. In view of the difficulty in the analysis, only the specialist case will be analysed. The obtained results indicate that the safe harbor can protect the endangered species under certain parametric restrictions.

One-dimensional cylindrical shock waves in non-ideal gas under magnetic field

Abstract: In the present paper, we analyze the evolutionary behavior of imploding strong shock waves propagating through a non-ideal gas in the presence of axial magnetic field. An evolution equation has been constructed by using the method based on the kinematics of one-dimensional motion of shock waves. The values of similarity exponents have been calculated by using the first order truncation approximation which describes the decay behavior of strong shocks. The approximate values of the similarity exponents are compared with the similarity exponents calculated by the CCW approximation, the exact similarity solution and perturbation technique.

Quasilinear elliptic systems with nonstandard growth and weak monotonicity

Abstract: We prove the existence of solutions for a quasilinear elliptic system $$\begin{aligned} \left\{ \begin{array}{ll} -\text {div}\,\sigma (x,u,Du)&{}=f(x,u,Du)\quad \text {in}\;\varOmega ,\\ u&{}=0\quad \text {on}\;\partial \varOmega . \end{array} \right. \end{aligned}$$ The results are obtained in Orlicz–Sobolev spaces by means of the Young measures.

Range convergence monotonicity for vector measures and range monotonicity of the mass

Abstract: We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the strict convergence implies the range convergence for strictly convex norms. In dimension 2 and for Euclidean spaces of any dimensions, we prove that the total variation of a vector measure is monotone with respect to the range.