Journal of the Egyptian Mathematical Society

Lassa fever is an infectious and zoonotic disease with incidence ranging between a hundred to three hundred thousand cases, with approximately five thousand deaths reported yearly in West Africa. This disease has become endemic in the Lassa belt of Sub-Saharan Africa, thus increasing the health burden in these regions including Nigeria. A deterministic mathematical model is presented to study the dynamics of Lassa fever in Nigeria. The model describes the transmission between two interacting hosts, namely the human and rodent populations. Using the cumulative number of cases reported by the Nigerian Centre for Disease Control within the first week of January 2020 through the eleventh week in 2021, we performed the model fitting and parameterization using the nonlinear least square method. The reproduction number $${\mathcal {R}}_{0}$$ R 0 which measures the potential spread of Lassa fever in the population is used to investigate the local and global stability of the system. The result shows that the model system is locally and globally asymptomatically stable whenever $${\mathcal {R}}_{0}<1$$ R 0 < 1 , otherwise it is unstable. Furthermore, the endemic equilibrium stability is investigated and the criteria for the existence of the phenomenon of bifurcation is presented. We performed the sensitivity analysis of each reproduction number parameter and solutions of the developed model are derived through an iterative numerical technique, a six-stage fifth-order Runge–Kutta method. Numerical simulations of the total infected human population $$(E_{h}+I_{h})$$ ( E h + I h ) under different numerical values (controlled parameters) are presented. The result from this study shows that combined controlled parameters made the total infected human population decline faster and thus reduces Lassa fever’s burden on the population.

In this paper, new forms of nano continuous functions in terms of the notion of nano Iα-open sets called nano Iα-continuous functions, strongly nano Iα-continuous functions and nano Iα-irresolute functions will be introduced and studied. We establish new types of nano Iα-open functions, nano Iα-closed functions and nano Iα-homeomorphisms. A comparison between these types of functions and other forms of continuity will be discussed. We prove the isomorphism between simple graphs via the nano continuity between them. Finally, we apply these topological results on some models for medicine and physics which will be used to give a solution for some real-life problems.

Topological indices are the molecular descriptors that describe the structures of chemical compounds. They are used in isomer discrimination, structure-property relationship, and structure-activity relations. The topological indices are used to predict certain physico-chemical properties such as boiling point, enthalpy of vaporization, and stability. In this paper, the inverse sum indeg index is studied. This index (ISI(G)) is defined as $\sum \frac {d_{u}d_{v}}{d_{u}+d_{v}}$∑dudvdu+dv. The inverse sum indeg index of some graph operations is computed. These operations are join, sequential join, cartesian product, lexicographic product, and corona operation.

In this paper, we study a multiple scales perturbation and numerical solution for vibrations analysis and control of a system which simulates the vibrations of a nonlinear composite beam model. System of second order differential equations with nonlinearity due to quadratic and cubic terms, excited by parametric and external excitations, are presented. The controller is implemented to control one frequency at primary and parametric resonance where damage in the mechanical system is probable. Active control is applied to the system. The multiple scales perturbation (MSP) method is implemented to obtain an approximate analytical solution. The stability analysis of the system is obtained by frequency response (FR). Bifurcation analysis is conducted using various control parameters such as natural frequency (ω₁), detuning parameter (σ₁), feedback signal gain (β), control signal gain (γ), and other parameters. The dynamic behavior of the system is predicted within various ranges of bifurcation parameters. All of the stable steady state (point attractor), stable periodic attractors, unstable steady state, and unstable periodic attractors are determined efficiently using bifurcation analysis. The controller’s influence on system behavior is examined numerically. To validate our results, the approximate analytical solution using the MSP method is compared with the numerical solution using the Runge-Kutta (RK) method of order four.

The current study investigates the combined response of the Darcy–Brinkman–Forchheimer and nonlinear thermal convection influence among other fluid parameters on Casson rheology (blood) flow through an inclined tapered stenosed artery with magnetic effect. Considering the remarkable importance of mathematical models to the physical behavior of fluid flow in human systems for scientific, biological, and industrial use, the present model predicts the motion and heat transfer of blood flow through tapered stenosed arteries under some underline conditions. The momentum and energy equations for the model were obtained and solved using the collocation method with the Legendre polynomial basis function. The expressions obtained for the velocity and temperature were graphed to show the effects of the Darcy–Brinkman–Forchheimer term, Casson parameters, and nonlinear thermal convection term among others. The results identified that a higher Darcy–Brinkman number slows down the blood temperature, while continuous injection of the Casson number decreases both velocity and temperature distribution.

This paper investigates the dynamics of an integer-order and fractional-order SIS epidemic model with birth in both susceptible and infected populations, constant recruitment, and the effect of fear levels due to infectious diseases. The existence, uniqueness, non-negativity, and boundedness of the solutions for both proposed models have been discussed. We have established the existence of various equilibrium points and derived sufficient conditions that ensure the local stability under two cases in both integer- and fractional-order models. Global stability has been vindicated using Dulac–Bendixson criterion in the integer-order model. The forward transcritical bifurcation near the disease-free equilibrium has been investigated. The effect of fear level on infected density has also been observed. We have done numerical simulation by MATLAB to verify the theoretical results, found the impact of fear level on the dynamic behaviour of the infected population, and obtained a bifurcation diagram concerning the constant recruitment and fear level. Finally, we have compared the stability of the population in integer and fractional-order systems.

In this study, we establish existence-uniqueness of a vector function in appropriate Sobolev-type space for a boundary value problem of a fifth-order operator differential equation. Proper conditions are obtained for the given problem to be well-posed. Much effort is devoted to develop the association between these conditions and the operator coefficients of the investigated equation. In this paper, accurate estimates of the norms of the intermediate derivatives operators are presented and used to determine the solvability conditions.