In this paper, we consider the existence of second-order damped vibration Hamiltonian systems with impulsive effects. We obtain some new existence theorems of solutions by using variational methods.

In this paper we study the oscillatory property of solutions for a class of partial difference equation with constant coefficients. In order to study the oscillation results, we find the regions of nonexistence of positive roots of its characteristic equation which is equivalent to the oscillation results. We derive some necessary and sufficient conditions by means of the envelope theory.

In this paper, we consider a ratio-dependent predator-prey system with multiple delays where the dynamics are logistic with the carrying capacity proportional to prey population. By choosing the sum \(\tau\) of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.

In the present paper, we study a new class of boundary value problems for Langevin quantum difference equations with multi-quantum numbers q-derivative nonlocal conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems. The existence and uniqueness of solutions is established by Banach's contraction mapping principle, while the existence of solutions is derived by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Examples illustrating the results are also presented.

In this paper, we give a fixed point theorem for multivalued mappings in a cone b-metric space without the assumption of normality on cones and generalize some attractive results in recent literature.

This paper introduces quasicompact-open topology on C(X) and compares this topology with the compact-open topology and the topology of uniform convergence. Then it examines submetrizability, metrizability, separability, and second countability of the quasicompact-open topology on C(X).

Our purpose in this paper is to consider a more generalized form of the Mittag-Leffler function. For this newly defined function, we obtain certain composition formulas with pathway fractional integral operators. We also point out some important special cases of the main results.

The purpose of this paper is to prove some new coupled common fixed point theorems for mappings defined on a set equipped with two S-metrics. We also provide illustrative examples in support of our new results. Meantime, we give an existence and uniqueness theorem of solution for a class of nonlinear integral equations by using the obtained result.

The aim of this paper is to investigate the solutions of Time-space fractional advection-dispersion equation with Hilfer composite fractional derivative and the space fractional Laplacian operator. The solution of the equation is obtained by applying the Laplace and Fourier transforms, in terms of Mittag-leffler function. The work by R. K. Saxena (2010) and Haung and Liu (2005) follows as particular case of our results.

By using the fixed point technique, we prove the stability of sixtic functional equations. Our results are studied and proved in the framework of fuzzy modular spaces (brie y, FM-spaces). The lower semi continuous (brie y, l.s.c.) and \(\beta\)-homogeneous are necessary conditions for this work.

The paper deals with fundamental inequalities for preinvex functions. The result relating to preinvex functions on the invex set that satisfies condition C shows that such functions are convex on every generated line segment. As an effect of that convexity, the paper provides symmetric forms of the most important inequalities which can be applied to preinvex functions.

The generalized type neural networks have always been a hotspot of research in recent years. This paper concerns the stabilization control of generalized type neural networks with piecewise constant argument. Through three types of stabilization control rules (single state stabilization control rule, multiple state stabilization control rule and output stabilization control rule), together with the estimate of the state vector with piecewise constant argument, several succinct criteria of stabilization are derived. The obtained results improve and extend some existing results. Two numerical examples are proposed to substantiate the effectiveness of the theoretical results.

Let \(X\) be a compact metric space and \(f\) be a continuous map from \(X\) into itself. In this paper, we introduce the concept of the sequence asymptotic average shadowing property, which is a generalization of the asymptotic average shadowing property. In the sequel, we prove some properties of the sequence asymptotic average shadowing property and investigate the relationship between the sequence asymptotic average shadowing property and transitivity.

In this paper, an extension of Caputo fractional derivative operator is introduced, and the extended fractional derivatives of some elementary functions are calculated. At the same time, extensions of some hypergeometric functions and their integral representations are presented by using the extended fractional derivative operator, linear and bilinear generating relations for extended hypergeometric functions are obtained, and Mellin transforms of some extended fractional derivatives are also determined.

In this paper, we consider a new class of boundary value problems of Caputo type fractional differential equations supplemented with classical/nonlocal Riemann-Liouville integral and flux boundary conditions and obtain some existence results for the given problems. The flux boundary condition \(x'(0) = b ^cD^\beta x(1)\) states that the ordinary flux \(x'(0)\) at the left-end point of the interval [0; 1] is proportional to a flux \(^cD^\beta x(1)\) of fractional order \(\beta \in (0; 1]\) at the right-end point of the given interval. The coupling of integral and flux boundary conditions introduced in this paper owes to the novelty of the work. We illustrate our results with the aid of examples. Our work not only generalizes some known results but also produces new results for specific values of the parameters involved in the problems at hand.

Hölder's inequality and its various generalizations are playing very important and basic role in different branches of modern mathematics. In this paper, we give some new monotonicity properties of generalized Hölder's inequalities and then we obtain some new refinements of generalized Hölder's inequalities.

The power law has been used to construct the derivative with fractional order in Caputo and Riemann- Liouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based upon the generalized Mittag-Leffler function, since the Mittag-Leffler function is more suitable in expressing nature than power function. In this paper, we applied their new finding to the model of groundwater flowing within an unconfined aquifer.

The purpose of this paper is to obtain several common fixed point theorems for four mappings in the setting of cone b-metric spaces over Banach algebras. The obtained results generalize, complement, and improve some results in the literature. Moreover, we give some supportive examples for our conclusions. In addition, an application in the solution of a class of equations is given to illustrate the superiority of the main results.

In this paper, an improved simulated annealing (SA) optimization algorithm is proposed for solving bilevel multiobjective programming problem (BLMPP). The improved SA algorithm uses a group of points in its operation instead of the classical point-by-point approach, and the rule for accepting a candidate solution that depends on a dominance based energy function is adopted in this algorithm. For BLMPP, the proposed method directly simulates the decision process of bilevel programming, which is different from most traditional algorithms designed for specific versions or based on specific assumptions. Finally, we present six different test problems to measure and evaluate the proposed algorithm, including low dimension and high dimension BLMPPs. The experimental results show that the proposed algorithm is a feasible and efficient method for solving BLMPPs.

In this paper, by using the concepts of \(\alpha\)-admissible mappings and simulation functions, we establish some fixed point results in the class of modular spaces. Our presented results generalize and improve many known results in literature. Some concrete examples are also provided to support the obtained results.

In this paper, we introduce two general algorithms (one implicit and one explicit) for finding a common element of the set of an equilibrium problem and the set of common fixed points of a nonexpansive semigroup \(\{T(s)\}_{s\geq 0}\) in Hilbert spaces. We prove that both approaches converge strongly to a common element \(x^*\) of the set of the equilibrium points and the set of common fixed points of \(\{T(s)\}_{s\geq 0}\). Such common element \(x^*\) is the unique solution of some variational inequality, which is the optimality condition for some minimization problem. As special cases of the above two algorithms, we obtain two schemes which both converge strongly to the minimum norm element of the set of the equilibrium points and the set of common fixed points of \(\{T(s)\}_{s\geq 0}\). The results obtained in the present paper improve and extend the corresponding results by Cianciaruso et al. [F. Cianciaruso, G. Marino, L. Muglia, J. Optim. Theory. Appl., 146 (2010), 491-509] and many others.

A modified iterative algorithm is presented based on the semi-implicit midpoint rule. Strong convergence analysis is demonstrated. Our method gives a unified framework related to the implicit midpoint rule. Our results improve and extend the corresponding results in the literature.

The Burgers' equation is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers' equation using the finite difference and collocation methods. With the temporal discretization of the equation using C-N scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical results of two different examples indicate the high accuracy and flexibility of the presented method.

In this paper, we introduced the notion of \(\alpha-\psi\)-type contractive mapping in PGM-spaces and established some new fixed point theorems in complete PGM-spaces. Finally, an example is given to support our main results.

In this paper, we study the existence of solutions for a class of rational systems of difference equations of order four in four-dimensional case \[x_{n+1} = \frac {x_{n-3}}{\pm 1\pm t_nz_{n-1}y_{n-2}x_{n-3}}, \qquad y_{n+1} =\frac{ y_{n-3}} {\pm 1\pm x_nt_{n-1}z_{n-2}y_{n-3}},\] \[z_{n+1} =\frac{ z_{n-3}} {\pm 1\pm y_nx_{n-1}t_{n-2}z_{n-3}}, \qquad t_{n+1} =\frac{ t_{n-3}} {\pm 1\pm z_ny_{n-1}x_{n-2}t_{n-3}},\] with the initial conditions are real numbers. Also, we study some behavior such as the periodicity and boundedness of solutions for such systems. Finally, some numerical examples are given to confirm our theoretical results and graphed by Matlab.

We establish existence results related to approximate fixed point property of special types of set-valued contraction mappings, in the setting of b-metric spaces. As consequences of the main theorem, we give some fixed point results which generalize and extend various fixed point theorems in the existing literature. A simple example illustrates the new theory. Finally, we apply our results to establishing the existence of solution for some differential and integral problems.

In this paper, we introduce a new iteration process and prove the convergence of this iteration process to a fixed point of contractive-like operators. We also present a data dependence result for such mappings. Our results unify and extend various results in the existing literature.

The aim of this paper is to present fuzzy optimal coincidence point results of fuzzy proximal quasi contraction and generalized fuzzy proximal quasi contraction of type-1 in the framework of complete non- Archimedean fuzzy metric space. Some examples are presented to support the results which are obtained here. These results also hold in fuzzy metric spaces when some mild assumption is added to the set in the domain of mappings which are involved here. Our results unify, extend and generalize various existing results in literature.

By virtue of the upper and lower solutions method, as well as the Schauder fixed point theorem, the existence of positive solutions to a class of q-fractional difference boundary value problems with \(\phi\)-Laplacian operator is investigated. The conclusions here extend existing results.

In this paper, we study the following fractional Schrödinger-poisson systems involving fractional Laplacian operator \[ \begin{cases} (-\Delta)^s + v(|x|)u + \phi(|x|,u)=f(|x|,u),\,\,\,\,&\ x\in \mathbb{R}^3,\\ (-\Delta)^t \phi = u^2,\,\,\,\,&\ x\in \mathbb{R}^3, \qquad (1) \end{cases} \] where \((-\Delta)^s(s \in (0; 1))\) and \((-\Delta)^t(t \in (0; 1))\) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions.

The aim of this paper is to introduce a new class of generalized metric spaces (called RS-spaces) that unify and extend, at the same time, Branciari’s generalized metric spaces and Jleli and Samet’s generalized metric spaces. Both families of spaces seen to be different in nature: on the one hand, Branciari’s spaces are endowed with a rectangular inequality and their metrics are finite valued, but they can contain convergent sequences with two different limits, or convergent sequences that are not Cauchy; on the other hand, in Jleli and Samet’s spaces, although the limit of a convergent sequence is unique, they are not endowed with a triangular inequality and we can found two points at infinite distance. However, we overcome such drawbacks and we illustrate that many abstract metric spaces (like dislocated metric spaces, b-metric spaces, rectangular metric spaces, modular metric spaces, among others) can be seen as particular cases of RS-spaces. In order to show its great applicability, we present some fixed point theorems in the setting of RS-spaces that extend well-known results in this line of research.

In this paper, a constraint shifting homotopy method for solving fixed point problems on nonconvex sets is proposed and the existence and global convergence of the smooth homotopy pathways is proved under some mild conditions. Compared with the previous results, the newly proposed homotopy method requires that the initial point needs to be only in the shifted feasible set not necessarily in the original feasible set, which relaxes the condition that the initial point must be an interior feasible point. Some numerical examples are also given to show the feasibility and effectiveness of our method.

The purpose of this note is to give a natural approach to the extensions of the Banach contraction principle in metric spaces endowed with a partial order, a directed graph or a binary relation in terms of extended quasi-metric. This novel approach is new and may open the door to other new fixed point theorems. The case of multivalued mappings is also discussed and an analogue result to Nadler's fixed point theorem in extended quasi-metric spaces is given.

This paper mainly studies the optimality conditions for a class of pessimistic trilevel optimization prob- lem, of which middle-level is a pessimistic problem. We firstly translate this problem into an auxiliary pessimistic bilevel optimization problem, by applying KKT approach for the lower level problem. Then we obtain a necessary optimality condition via the differential calculus of Mordukhovich. Finally, we obtain an existence theorem of optimal solution by direct method.

In the present paper, we generalize the concept of well-posedness to a generalized hemivariational in- equality, give some metric characterizations of the \(\alpha\)-well-posed generalized hemivariational inequality, and derive some conditions under which the generalized hemivariational inequality is strongly \(\alpha\)-well-posed in the generalized sense. Also, we show that the \(\alpha\)-well-posedness of the generalized hemivariational inequality is equivalent to the \(\alpha\)-well-posedness of the corresponding inclusion problem.

In this paper, we present a fixed point theorem for multivalued mappings on generalized metric space in the sense of Jleli and Samet [M. Jleli, B. Samet, Fixed Point Theory Appl., 2015 (2015), 61 pages]. In fact, we obtain as a spacial case both b-metric version and dislocated metric version of Feng-Liu's fixed point result.

The Mellin integral transform is an important tool in mathematics and is closely related to Fourier and bi-lateral Laplace transforms. In this article we aim to investigate the Mellin transform in a class of quaternions which are coordinates for rotations and orientations. We consider a set of quaternions as a set of generalized functions. Then we provide a new definition of the cited Mellin integral on the provided set of quaternions. The attributive Mellin integral is one-to-one, onto and continuous in the quaternion spaces. Further properties of the discussed integral are given on a quaternion context.

In this article, the sum of a monotone mapping, an inverse strongly monotone mapping, and a strictly pseudocontractive mapping are investigated based on two regularization iterative algorithms. Strong convergence analysis of the two iterative algorithms is obtained in the framework of real Hilbert spaces.

By use of a new viscosity approximation method, we construct an explicit iterative algorithm for finding common fixed points of a sequence of nonexpansive mappings with weakly contractive mappings in the framework of Banach spaces. A strong convergence theorem is obtained for solving a kind of variational inequality problems. Our results improve and extend the corresponding ones of other authors with related interest.

In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0; 1];X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.

The purpose of this article is to investigate fixed point problems of a nonexpansive mapping, solutions of quasi variational inclusion problem, and solutions of a generalized equilibrium problem based on a splitting method. Our convergence theorems are established under mild restrictions imposed on the control sequences. The main results improve and extend the recent corresponding results.

This paper studies a Filippov predator-prey system, where chemical control strategies are proposed and analyzed. Initially, the exact sliding segment and its domains are addressed. Then the existence and stability of the regular, virtual, pseudo-equilibria and tangent points are discussed. It shows that two regular equilibria and a pseudo-equilibrium can coexist. By employing theoretical and numerical techniques several kinds of bifurcations are investigated, such as sliding bifurcations related to the boundary node (focus) bifurcations, touching bifurcations, sliding crossing bifurcation and buckling bifurcations (or sliding switching). Furthermore, it makes comparison of the obtained results with previous studies for the Filippov predator-prey system without control strategies. Some biological implications of our results with respect to pest control are also given.

In this paper, we use weakly commuting and weakly compatible conditions of self-mapping pairs, prove some new common fixed point theorems for three pairs of self-maps in the framework of generalized metric spaces. The results presented in this paper generalize the well known comparable results in the literature due to Abbas et al. [M. Abbas, T. Nazir, R. Saadati, Adv. Difference Equ., 2011 (2011), 20 pages]. We also provide illustrative examples in support of our new results.

In this paper, we investigate the quadratic \(\alpha\)-functional equation \[2f(x) + 2f(y) = f(x - y) + \alpha^{-2}f(\alpha(x + y)); \quad(1)\] \[2f(x) + 2f(y) = f(x + y) + \alpha^{-2}f(\alpha(x - y));\quad (2)\] where \(\alpha\) is a fixed nonzero real or complex number with \(\alpha^{-1}\neq \pm\sqrt{3}\). Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic \(\alpha\)-functional equations (1) and (2) in Banach spaces.

In this paper, we study the existence of positive solutions to the nonlinear fractional order singular and semipositone nonlocal boundary value problem \[ \begin{cases} \mathfrak{D}^\alpha_{0^+}u(t)+f(t,u(t))=0,\,\,\,\,\, 0<t<1,\\ u(0)=u'(0)=...=u^{(n-2)}(0)=0,\,\,\,\,\, u(1)=\mu\int^1_0 u(s)ds. \end{cases} \] by using the Leray-Schauder nonlinear alternative and a fixed-point theorem on cones, where \(0 < \mu < \alpha; 2 \leq n - 1 < \alpha \leq n, \mathfrak{D}^\alpha_{0^+}\) is the standard Riemann-Liouville derivative, and f(t; u) is semipositone and may be singular at u = 0.

In this article, we propose an iteration methods for finding a split equality common fixed point of asymptotically nonexpansive semigroups in Banach spaces. The weak and strong convergence theorems of the iteration scheme proposed are obtained. As application, we shall utilize our results to study the split equality variational inequality problems to support the main results. The results presented in the article are new and improve and extend some recent corresponding results.

In this paper we give some properties of a class of intuitionistic fuzzy metrics which is called strong. This new class includes the class of stationary intuitionistic fuzzy metrics. So we examine the relationship between strong intuitionistic fuzzy metric and stationary intuitionistic fuzzy metric.

The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain assumptions imposed on the parameters. As applications, we use our main results to solve fixed point problems of strict pseudocontractions in Hilbert spaces and variational inequality problems in Hilbert spaces. Finally, we also give one numerical example to support our main results.

In this paper, we introduce and analyze a hybrid extragradient algorithm for solving bilevel pseudomonotone variational inequalities with multiple solutions in a real Hilbert space. The proposed algorithm is based on Korpelevich's extragradient method, Mann's iteration method, hybrid steepest-descent method, and viscosity approximation method (including Halpern's iteration method). Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is derived.

Through solving equations step by step and by using the generalized Banach fixed point theorem, under simple conditions, the authors present the existence and uniqueness theorem of the iterative solution for nonlinear advection-reaction-diffusion equations with impulsive effects. An explicit iterative scheme for the solution is also derived. The results obtained generalize and improve some known results.

In this paper, we prove the analog to Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings in complete hyperbolic metric spaces uniformly convex. In the linear case, this result is refined. Indeed, we prove that if X is a Banach space uniformly convex in every direction endowed with a graph \(G\), then every \(G\)-nonexpansive mapping \(T : A \rightarrow A\), where \(A\) is a nonempty weakly compact convex subset of \(X\), has a fixed point provided that there exists \(u_0 \in A\) such that \(T(u_0)\) and \(u_0\) are \(G\)-connected.

In this paper, we introduce new types of Caristi fixed point theorem and Caristi-type cyclic maps in a metric space with a partial order or a directed graph. These types of mappings are more general than that of Du and Karapinar [W.-S. Du, E. Karapinar, Fixed Point Theory Appl., 2013 (2013), 13 pages]. We obtain some fixed point results for such Caristi-type maps and prove some convergence theorems and best proximity results for such Caristi-type cyclic maps. It should be mentioned that in our results, all the optional conditions for the dominated functions are presented and discussed to our knowledge, and the replacing of \(d(x; Tx)\) by \(\min\{d(x; Tx); d(Tx; Ty)\}\) endowed with a graph makes our results strictly more general. Many recent results involving Caristi fixed point or best proximity point can be deduced immediately from our theory. Serval applications and examples are presented making effective the new concepts and results. Two analogues for Banach-type contraction are also provided.

In this note, we discuss the definition of the multivalued weak contraction mappings defined in a metric space endowed with a graph as introduced by Hanjing and Suantai[A. Hanjing, S. Suantai, Fixed Point Theory Appl., 2015 (2015), 10 pages]. In particular, we show that this definition is not correct and give the correct definition of the multivalued weak contraction mappings defined in a metric space endowed with a graph. Then we prove the existence of coincidence points for such mappings.

In this paper, we establish an existence result for the (GSVQEP) without assuming that the dual of the ordering cone has a weak star compact base and give an example to show our existence theorem is different from the main result of Long et al. [X. J. Long, N. J. Huang, K. L. Teo, Math. Comput. Modelling, 47 (2008), 445-451]. Furthermore, we introduce a concept of Hadamard-type well-posedness for the (GSVQEP) and establish sufficient conditions of Hadamard-type well-posedness for the (GSVQEP).

In this paper, we establish certain new fixed point theorems for contractive inequalities using an auxiliary function which dominates the ordinary metric function. As application, we derive some recent known results as corollaries. Certain interesting consequences of our results are also presented. An example is given to illustrate the usability of the obtained results.

The purpose of this paper is to introduce the notions of (\(\psi,\phi\))-type contractions and (\(\psi,\phi\))-type Suzuki contractions and to establish some new fixed point theorems for such kind of mappings in the setting of complete metric spaces. The results presented in the paper are an extension of the Banach contraction principle, Suzuki contraction theorem, Jleli and Samet fixed point theorem, Piri and Kumam fixed point theorem.

In this paper, quasi-variational inclusion and fixed point problems are investigated based on a general iterative process. Strong convergence theorems are established in the framework of Hilbert spaces.

In this paper, we introduce and analyze a multi-step hybrid steepest-descent algorithm by combining Korpelevich's extragradient method, viscosity approximation method, hybrid steepest-descent method, Mann's iteration method and gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces. Strong convergence was established.

This paper studies the existence and stability of weighted Nash equilibria for multiobjective population games. By constructing a Nash's mapping, the existence of weighted Nash equilibria is established. Furthermore, via the generic continuity method, each weighted Nash equilibrium is shown to be stable for most of multiobjective population games when weight combinations and payoff functions are simultaneously perturbed. Besides, this leads to the stability of Nash equilibria for classical population games with the perturbed payoff functions. These results play cornerstone role in the research concerning multiobjective population games.

In this paper, we introduce the concept of generalized \(\alpha-\eta-\psi-\varphi-F-\)contraction type mappings where \(\psi\) is the altering distance function and \(\varphi\) is the ultra altering distance function. The unique fixed point theorems for such mappings in the setting of \(\alpha-\eta-\)-complete metric spaces are proven. We also assure the fixed point theorems in partially ordered metric spaces. Moreover, the solution of the integral equation is obtained using our main result.

Some Epidemic models with fractional derivatives were proved to be well-defined, well-posed and more accurate (Brockmann et al. [D. Brockmann, L. Hufnagel, Phys. Review Lett., 98 (2007), 17-27]; Doungmo Goufo et al. [E. F. Doungmo Goufo, R. Maritz, J. Munganga, Adv. Diff. Equ., 2014 (2014), 9 pages]; Pooseh et al. [S. Pooseh, H. S. Rodrigues, D. F. M. Torres, In: Numerical Analysis and Applied Mathematics, ICNAAM, American Institute of Physics, Melville, (2011), 739-742]), compared to models with the conventional derivative. In this paper, an Ebola epidemic model with non linear transmission is analyzed. The model is expressed with the conventional time derivative with a new parameter included, which happens to be fractional. We proved that the model is well-defined, well-posed. Moreover, conditions for boundedness and dissipativity of the trajectories are established. Exploiting the generalized Routh-Hurwitz Criteria, existence and stability analysis of equilibrium points for Ebola model are performed to show that they are strongly dependent on the non-linear transmission. In particular, conditions for existence and stability of a unique endemic equilibrium to the Ebola system are given. Finally, numerical simulations are provided for particular expressions of the non-linear transmission (with parameters \(\kappa = 0:01, \kappa = 1\) and \(p = 2\)). The obtained simulations are in concordance with the usual threshold behavior. The results obtained here are significant for the fight and prevention against Ebola haemorrhagic fever that has so far exterminated hundreds of families and is still infecting many people in West-Africa.

In this paper, we prove that the Ricci tensor of an almost Kenmotsu 3-h-manifold is cyclic-parallel if and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space \(\mathbb{H}^3(-1) \) or the Riemannian product \(\mathbb{H}^2(-4) \times \mathbb{R}\).