A novel SVIR epidemic model with jumps for understanding the dynamics of the spread of dual diseases.

The emergence of multi-disease epidemics presents an escalating threat to global health. In response to this serious challenge, we present an innovative stochastic susceptible-vaccinated-infected-recovered epidemic model that addresses the dynamics of two diseases alongside intricate vaccination strategies. Our novel model undergoes a comprehensive exploration through both theoretical and numerical analyses. The stopping time concept, along with appropriate Lyapunov functions, allows us to explore the possibility of a globally positive solution. Through the derivation of reproduction numbers associated with the stochastic model, we establish criteria for the potential extinction of the diseases. The conditions under which one or both diseases may persist are explained. In the numerical aspect, we derive a computational scheme based on the Milstein method. The scheme will not only substantiate the theoretical results but also facilitate the examination of the impact of parameters on disease dynamics. Through examples and simulations, we have a crucial impact of varying parameters on the system's behavior.

New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations with Nonlinear Neutral Terms.

In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.

A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host.

Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents. At the same time, the transmission of the infection to the human host is caused by domestic animals that represent in the habitat the intermediate host. In this study, we review the currently collected information about coronaviruses and establish a model of differential equations with piecewise constant arguments to discuss the spread of the infection from the natural host to the intermediate, and from them to the human host, while we focus on the potential spillover of bat-borne coronaviruses. The local stability of the positive equilibrium point of the model is considered via the Linearized Stability Theorem. Besides, we discuss global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time t and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates the Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings.

Entropy generation for exact irreversibility analysis in the MHD channel flow of Williamson fluid with combined convective-radiative boundary conditions.

The scrutinization of entropy optimization in the various flow mechanisms of non-Newtonian fluids with heat transfer has been incredibly enhanced. Through the investigation of irreversibility sources in the steady flow of a non-Newtonian Willaimson fluid, an analysis of entropy generation is carried out in this current work. The current study has an essential aspect of investigating the heat transfer mechanism with flow phenomenon by considering convective-radiative boundary conditions. A horizontal MHD channel is assumed with two parallel plates to develop a mathematical model for the flow phenomenon by considering the variable viscosity of the fluid. The contribution of physical impacts of thermal radiation, Joule heating, and viscous dissipation is interpolated in the constitutive energy equation. The complete flow of the current analysis is established in the form of ordinary differential equations which further take the form of the dimensionless system through the contribution of the similarity variables. A graphical scrutinization of the physical features of the flow phenomenon in relation to the pertinent parameters is proposed. This study reveals that the higher magnitude of radiation parameter and Brinkman number dominates the system's entropy. Moreover, the temperature distribution experiences an increasing mechanism with improved conduction-radiation parameter at the lower plate.

Instability analysis for MHD boundary layer flow of nanofluid over a rotating disk with anisotropic and isotropic roughness.

The study focuses on the instability of local linear convective flow in an incompressible boundary layer caused by a rough rotating disk in a steady MHD flow of viscous nanofluid. Miklavcic and Wang's (Miklavcic and Wang, 2004) [9] MW roughness model are utilized in the presence of MHD of Cu-water nanofluid with enforcement of axial flows. This study will investigate the instability characteristics with the MHD boundary layer flow of nanofluid over a rotating disk and incorporate the effects of axial flow with anisotropic and isotropic surface roughness. The resulting ordinary differential equations (ODEs) are obtained by using von Kàrmàn (Kármán, 1921) [3] similarity transformation on partial differential equations (PDEs). Subsequently, numerical solutions are obtained using the shooting method, specifically the Runge-Kutta technique. Steady-flow profiles for MHD and volume fractions of nanoparticles are analyzed by the partial-slip conditions with surface roughness. Convective instability for stationary modes and neutral stability curves are also obtained and investigated by the formulation of linear stability equations with the MHD of nanofluid. Linear convective growth rates are utilized to analyze the stability of magnetic fields and nanoparticles and to confirm the outcomes of this analysis. Stationary disturbances are also considered in the energy analysis. The investigation indicates the correlation between instability modes Type I and Type II, in the presence of MHD, nanoparticles, and the growth rates of the critical Reynolds number. An integral energy equation enhances comprehension of the fundamental physical mechanisms. The factors contributing to convective instability in the system are clarified using this approach.

Effects of variable magnetic field and partial slips on the dynamics of Sutterby nanofluid due to biaxially exponential and nonlinear stretchable sheets.

Based on both the characteristics of shear thinning and shear thickening fluids, the Sutterby fluid has various applications in engineering and industrial fields. Due to the dual nature of the Sutterby fluid, the motive of the current study is to scrutinize the variable physical effects on the Sutterby nanofluid flow subject to shear thickening and shear thinning behavior over biaxially stretchable exponential and nonlinear sheets. The steady flow mechanism with the variable magnetic field, partial slip effects, and variable heat source/sink is examined over both stretchable sheets. The analysis of mass and heat transfer is carried out with the mutual impacts of thermophoresis and Brownian motion through the Buongiorno model. Suitable transformations for both exponential and nonlinear sheets are implemented on the problem's constitutive equations. As a result, the nonlinear setup of ordinary differential equations is acquired which is further numerically analyzed through the bvp4c technique in MATLAB. The graphical explanation of temperature, velocity, and concentration distributions exhibits that the exponential sheet provides more significant results as compared to the nonlinear sheet. Further, this study revealed that for the shear thickening behavior of Sutterby nanofluid, the increasing values of Deborah number increase the axial velocity.

Fractional Nadeem trigonometric non-Newtonian (NTNN) fluid model based on Caputo-Fabrizio fractional derivative with heated boundaries.

The fractional operator of Caputo-Fabrizio has significant advantages in various physical flow problems due to the implementations in manufacturing and engineering fields such as viscoelastic damping in polymer, image processing, wave propagation, and dielectric polymerization. The current study has the main objective of implementation of Caputo-Fabrizio fractional derivative on the flow phenomenon and heat transfer mechanism of trigonometric non-Newtonian fluid. The time-dependent flow mechanism is assumed to be developed through a vertical infinite plate. The thermal radiation's effects are incorporated into the analysis of heat transfer. With the help of mathematical formulations, the physical flow system is expressed. The governing equations of the flow system acquire the dimensionless form through the involvement of the dimensionless variables. The application of Caputo-Fabrizio derivative is implemented to achieve the fractional model of the dimensionless system. An exact solution of the fractional-based dimensionless system of the equations is acquired through the technique of the Laplace transform. Physical interpretation of temperature and velocity distributions relative to the pertinent parameters is visualized via graphs. The current study concludes that the velocity distributions exhibit an accelerating nature corresponding to the increasing order of the fractional operator. Moreover, the graphical results are more significant corresponding to the greater time period.

The flow of an Eyring Powell Nanofluid in a porous peristaltic channel through a porous medium.

In a porous medium, we have examined sinusoidal two-dimensional transport enclosed porous peristaltic boundaries having an Eyring Powell fluid with a water containing [Formula: see text]. The determining momentum and temperature equations are solved semi-analytically by using regular perturbation method and Mathematica. In present research only free pumping case and small amplitude ratio is studied. Mathematical and pictorial consequences are investigated for distinct physical parameters of interest like porosity, viscosity, volume fraction and permeability to check the effects of flow velocity and temperature.

Investigation of fractal-fractional HIV infection by evaluating the drug therapy effect in the Atangana-Baleanu sense.

In this paper, we apply the fractal-fractional derivative in the Atangana-Baleanu sense to a model of the human immunodeficiency virus infection of CD$ 4^{+} $ T-cells in the presence of a reverse transcriptase inhibitor, which occurs before the infected cell begins producing the virus. The existence and uniqueness results obtained by applying Banach-type and Leray-Schauder-type fixed-point theorems for the solution of the suggested model are established. Stability analysis in the context of Ulam's stability and its various types are investigated in order to ensure that a close exact solution exists. Additionally, the equilibrium points and their stability are analyzed by using the basic reproduction number. Three numerical algorithms are provided to illustrate the approximate solutions by using the Newton polynomial approach, the Adam-Bashforth method and the predictor-corrector technique, and a comparison between them is presented. Furthermore, we present the results of numerical simulations in the form of graphical figures corresponding to different fractal dimensions and fractional orders between zero and one. We analyze the behavior of the considered model for the provided values of input factors. As a result, the behavior of the system was predicted for various fractal dimensions and fractional orders, which revealed that slight changes in the fractal dimensions and fractional orders had no impact on the function's behavior in general but only occur in the numerical simulations.

Stochastic dynamics of influenza infection: Qualitative analysis and numerical results.

In this paper, a novel influenza $ \mathcal{S}\mathcal{I}_N\mathcal{I}_R\mathcal{R} $ model with white noise is investigated. According to the research, white noise has a significant impact on the disease. First, we explain that there is global existence and positivity to the solution. Then we show that the stochastic basic reproduction $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}} {_r} $ is a threshold that determines whether the disease is cured or persists. When the noise intensity is high, we get $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} < 1 $ and the disease goes away; when the white noise intensity is low, we get $ {{\underset{\scriptscriptstyle\centerdot}{\text{R}}}}{_r} > 1 $, and a sufficient condition for the existence of a stationary distribution is obtained, which suggests that the disease is still there. However, the main objective of the study is to produce a stochastic analogue of the deterministic model that we analyze using numerical simulations to get views on the infection dynamics in a stochastic environment that we can relate to the deterministic context.

Dynamical properties of a novel one dimensional chaotic map.

In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu > 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.

A mathematical model for the dynamics of SARS-CoV-2 virus using the Caputo-Fabrizio operator.

The pandemic of SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics which spread worldwide through human interactions. The current study is focusing on the investigation and analysis of a fractional-order epidemic model that discusses the temporal dynamics of the SARS-CoV-2 virus in a community. It is well known that symptomatic and asymptomatic individuals have a major effect on the dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups of the population. Further, we assume that the vaccine confers permanent immunity because multiple vaccinations have commenced across the globe. The new fractional-order model for the transmission dynamics of SARS-CoV-2 virus is formulated via the Caputo-Fabrizio fractional-order approach with the maintenance of dimension during the process of fractionalization. The theory of fixed point will be used to show that the proposed model possesses a unique solution whereas the well-posedness (bounded-ness and positivity) of the fractional-order model solutions are discussed. The steady states of the model are analyzed and the sensitivity analysis of the basic reproductive number is explored. Moreover to parameterize the model a real data of SARS-CoV-2 virus reported in the Sultanate of Oman from January 1st, 2021 to May 23rd, 2021 are used. We then perform the large scale numerical findings to show the validity of the analytical work.

On periodic solutions of a discrete Nicholson's dual system with density-dependent mortality and harvesting terms.

In this study, we discuss the existence of positive periodic solutions of a class of discrete density-dependent mortal Nicholson's dual system with harvesting terms. By means of the continuation coincidence degree theorem, a set of sufficient conditions, which ensure that there exists at least one positive periodic solution, are established. A numerical example with graphical simulation of the model is provided to examine the validity of the main results.

Study of dynamic behaviour of psychological stress during COVID-19 in India: A mathematical approach.

In this study, a new attempt has been made using mathematical modelling to study dynamic behaviour and estimate the final size of spread of the psychological stress arising due to sudden outbreak of COVID-19 in India. The proposed mathematical model examines and includes different behaviours of transition from one process to another in current situation and study their propagation mode. We propose a mathematical model, where two different type of psychological stresses occur due to COVID-19 situation and its impact on people's life such as their mental well being and happiness. We present some sufficient conditions for the vanishing or spreading of the psychological stress through qualitative and quantitative analysis. The basic reproduction number ( R 0 ) of the model is computed and the local and the global stabilities of different equilibria are studied. Moreover, to better understand the level of psychological stress and decreasing mental well-being during the COVID-19 outbreak in India, we also conducted an online survey. Our findings establish several factors associated with level of psychological impact and mental health status. Based on the empirical analysis, we found that psychological stress has a significant negative influence on mental well being. Further, this study confirms that coping strategies with stress have significantly contributed towards the betterment in the mental well-being of the people. Numerical simulations are also given to illustrate the theoretical results. The results of the present study can be generalized to the society, Government, and others that they can adopt different strategies to avoid stressful situations during COVID-19 outbreak. The findings suggest that policy-makers, Government officials should focus on coping strategies to combat with pandemic disease.

Existence and stability of nonlinear discrete fractional initial value problems with application to vibrating eardrum.

It is well known that Newton's second law can be applied in various biological processes including the behavior of vibrating eardrums. In this work, we consider a nonlinear discrete fractional initial value problem as a model describing the dynamic of vibrating eardrum. We establish sufficient conditions for the existence, uniqueness, and Hyers-Ulam stability for the solutions of the proposed model. To examine the validity of our findings, a concrete example of forced eardrum equation along with numerical simulation is analyzed.

Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives.

We state and prove new generalized Lyapunov-type and Hartman-type inequalities for a conformable boundary value problem of order α∈(1,2] with mixed non-linearities of the form (Tαax)(t)+r1(t)|x(t)|η-1x(t)+r2(t)|x(t)|δ-1x(t)=g(t),t∈(a,b), satisfying the Dirichlet boundary conditions x(a)=x(b)=0 , where r1 , r2 , and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0<η<1<δ<2 . Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative Tαa is replaced by a sequential conformable derivative Tαa∘Tαa , α∈(1/2,1] . The potential functions r1 , r2 as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.