In this paper, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model from mathematical epidemiology by incorporating a vaccinated compartment, V, accounting for an imperfect vaccine with waning efficacy over time. The SIRSV-model divides population into four compartments and introduces periodic re-vaccination immunity. efficiency of is assumed to decay time passed since vaccination. Periodic re-vaccinations are applied population. We develop partial differential...

Being an example for a relaxation oscillator, the FitzHugh-Nagumo model has been widely employed describing generation of action potentials. In this paper, we begin with biological interpretation what subsequent mathematical and numerical analyses entail. The interaction between potential variable recovery is then revisited through linear stability analysis around equilibrium local conditions are determined. Analytical results compared simulations. study aims to show alternative approach...

In this study, we consider high-order nonlinear ordinary differential equations with the initial and boundary conditions.These kinds of are essential tools for modelling problems in physics, biology, neurology, engineering, ecology, economy, astrophysics, physiology so forth.Each mentioned described by one following specific physical conditions: Riccati, Duffing, Emden-Fowler, Lane Emden type equations.We seek approximate solution these special means a operational matrix technique, called...

Laguerre collocation method is applied for solving a class of the Fredholm integro-differential equations with functional arguments. This transforms considered problem to matrix equation which corresponds system linear algebraic equations. The reliability and efficiency proposed scheme are demonstrated by some numerical experiments. Also, approximate solutions corrected using residual correction method.

Abstract There is currently an undeniable demand for solutions to environmental issues, especially water pollution. Water essential life and lakes constitute a big portion of sources. In this study, we introduce modified numerical approach dynamic ecological model focused on lake pollution problem. The includes three connected with certain parameters unknown functions such as quantities volumes. First, preliminary mathematical analysis the variables each presented taking into account system...

The development of science and technology provides significant changes to the teaching learning process. use smartphone with various operating system platforms Android is also widely used in world education. Various types applications were created support process at school outside school. purpose this research create an alternative media form interactive animation application that utilizes on material or topic discussion elements chemical experiments eyes chemistry lessons. This...

Abstract In this study, an effective numerical technique has been introduced for finding the solutions of first-order integro-differential equations including neutral terms with variable delays. The problem defined by using initial value. Then, alternative method solving these type problems. is expressed fundamental matrices, Laguerre polynomials their matrix forms. Besides, solution obtained collocation points regard to reduced system algebraic and series.

In this study, we consider some nonlinear partial integro-differential equations.Most of these equations are used as mathematical models in many problems physics, biology, chemistry, engineering, and other areas.Our main purpose is to propose a new numerical method based on the Laguerre Taylor polynomials, called matrix collocation method, for solution mentioned under initial or boundary conditions.To show effectiveness approach, examples along with error estimations illustrated by tables figures.

Partial integro-differential equations occur in many fields of science and engineering.Besides, the class parabolic-type differential is modelled compression poro-viscoelastic media, reaction-diffusion problems nuclear reactor dynamics.In recent years, most mathematical models used physics, biology, chemistry engineering are based on integral equations.In this work, we propose a new effective numerical scheme Laguerre matrix-collocation method to obtain approximate solution one dimensional...

The theory and applications of differential equations have played an essential role both in the development mathematics exploring new horizons applied sciences [...]

The COVID-19 pandemic led to widespread interest in epidemiological models. In this context the role of vaccination influencing spreading disease is particular interest. There has also been a lot debate on non-pharmaceutical interventions such as disinfection surfaces. We investigate mathematical model for spread which includes both imperfect and infection due virus environment. latter studied with help two phenomenological models force infection. one these we find that backward bifurcations...

In this study, we develop a novel matrix collocation method based on the Laguerre polynomials to find approximate solutions of some parabolic delay differential equations with integral terms subject appropriate initial and boundary conditions.The reduces solution mentioned equation which corresponds system algebraic unknown coefficients.Besides, error analysis together numerical results are performed illustrate efficiency our computationally.

In this study, we propose a modified Laguerre collocation method based on operational matrix technique to solve 1‐dimensional parabolic convection‐diffusion problems arising in applied sciences. The transforms the equation and mixed conditions of problem into with unknown coefficients by means points matrices. solution yields function. Thereby, approximate is obtained truncated series form. Also, illustrate usefulness applicability method, apply it test together residual error estimation...

In this study, by means of the matrix relations between Laguerre polynomials, and their derivatives, a novel method based on collocation points is modified developed for solving class second-order nonlinear ordinary differential equations having quadratic cubic terms, via mixed conditions. The reduces solution equation to corresponding system algebraic with unknown coefficients. Also, some illustrative examples along an error analysis residual function are included demonstrate validity...

This paper presents a numerical method for the approximate solution of mthorder linear delay difference equations with variable coefficients under mixed conditions in terms Laguerre polynomials. The aim this article is to present an efficient procedure solving mth-order coefficients. Our depends mainly on series expansion approach. transforms and given into matrix equation which corresponds system algebraic equation. reliability efficiency proposed scheme are demonstrated by some experiments...