The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two

Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions.Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications.Mathematical modelling has been widely used in order to better understand the transmission,treatment,and prevention of infectious diseases.Herein,we study the dynamics of a human immunodeficiency virus(HIV)infection model with four variables:S(t),I(t),C(t),and A(t)the susceptible individuals;HIV infected individuals(with no clinical symptoms of AIDS);HIV infected individuals(under ART with a viral load remaining low),and HIV infected individuals with two different incidence functions(bilinear and saturated incidence functions).A novel numerical scheme called the continuous Galerkin-Petrov method is implemented for the solution of themodel.The influence of different clinical parameters on the dynamical behavior of S(t),I(t),C(t)and A(t)is described and analyzed.All the results are depicted graphically.On the other hand,we explore the time-dependent movement of nanofluid in porous media on an extending sheet under the influence of thermal radiation,heat flux,hall impact,variable heat source,and nanomaterial.The flow is considered to be 2D,boundary layer,viscous,incompressible,laminar,and unsteady.Sufficient transformations turn governing connected PDEs intoODEs,which are solved using the proposed scheme.To justify the envisaged problem,a comparison of the current work with previous literature is presented.

Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.

Global dynamics of an age-structured viral infection model with general incidence function and absorption

In this paper, we propose an age-structured viral infection model with general incidence function that takes account of the loss of viral particles due to their absorption into susceptible cells. The proposed model is described by partial differential and ordinary differential equations. We first show that the model is mathematically and biologically well-posed. Furthermore, the uniform persistence and the global behavior of the model are investigated. Moreover, the age-structured models and results presented in many previous studies are improved and generalized.

Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes

Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.

Analysis of within-host CHIKV dynamics models with general incidence rate

In this paper we study the stability analysis of two within-host Chikungunya virus （CHIKV） dynamics models. The incidence rate between the CHIKV and the uninfected mouocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes （i） latently infected monocytes which do not generate CHIKV and （ii） actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

Modeling the transmission dynamics of a time-delayed epidemic model with saturated treatment rate

In this paper,an attempt has been made to explore a new delayed epidemiological model assuming that the disease is transmitted among the susceptible population and possessing nonlinear incidence function along with a saturated treatment rate.Due attention is paid to the positivity and boundedness of the solutions and the bifurcation of the dynamical system as well.Basic reproduction number is being calculated,and considering the latent period as a bifurcation parameter,it has been examined that a Hopf-bifurcation occurs near the endemic equilibrium point while the parameter attains critical values.We have also discussed the stability and direction of Hopf-bifurcation near the endemic equilibrium point,the global stability analysis and the optimal control theory.We conclude that the system reveals chaotic dynamics through a specific time-delay value.Numerical simulations are being performed in order to explain the accuracy and effectiveness of the acquired theoretical results.

Mortality of Amur tigers:The more things change,the more they stay the same

Poaching as well as loss of habitat and prey are identified as causes of tiger population declines.Although some studies have examined habitat requirements and prey availability,few studies have quantified cause-specific mortality of tigers.We used cumulative incidence functions(CIFs)to quantify cause-specific mortality rates of tigers,expanding and refining earlier studies to assess the potential impact of a newly emerging disease.To quantify changes in tiger mortality over time,we re-examined data first collected by Goodrich et al.(2008;study period 1:1992–2004)as well as new telemetry data collected since January 2005(study period 2:2005–2012)using a total of 57 tigers(27 males and 30 females)monitored for an average of 747 days(range 26–4718 days).Across the entire study period(1992 to 2012)we found an estimated average annual survival rate of 0.75 for all tigers combined.Poaching was the primary cause of mortality during both study periods,followed by suspected poaching,distemper and natural/unknown causes.Since 2005,poaching mortality has remained relatively constant and,if combined with suspected poaching,may account for a loss of 17–19%of the population each year.Canine distemper virus(CDV)may be an additive form of mortality to the population,currently accounting for an additional 5%.Despite this relatively new source of mortality,poaching remains the main threat to Amur tiger survival and,therefore,population growth.

An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data

This paper proposes a flexible additive-multiplicative Cox-Aalen hazard model which allows time-varying covariate effects for the subdistribution in a competing risks study.Weigh ted estimating equation approaches under an covariates-dependent adjusted weight by fitting the Cox proportional hazard model for the censoring distribution are established for inference on the model parametric and nonparametric components.In addition,large number properties are presented and the finite sample behavior of the proposed estimators is evaluated through simulation studies,estimators from the proposed method perform satisfactorily on reduction of the bias.The authors apply our model to a competing risks data set from a tamoxifen trail for breast cancer study.

MATHEMATICAL ANALYSIS OF AN IMPROVED HEPATITIS B VIRUS MODEL

A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-free and infection equilibria is discussed, respectively. Further, the existence of an orbitally asymptotically stable periodic orbit is also studied. By means of the theory of competitive systems and compound matrices, sufficient conditions are derived for the global stability of the infection-free and infection equilibria, respectively. At last, numerical simulations are carried out to illustrate the main results.