This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state...This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state,and show that the chemotactic flux is the key mechanism for pattern formation.Then,we treat the chemotaxis coefficient as a bifurcation parameter to obtain the asymptotic expressions of steady states.Based on this,we derive the sufficient conditions for the stability of one-step pattern,and prove the metastability of two or more step patterns.All the analytical results are demonstrated by numerical simulations.展开更多
We consider in this research an age-structured alcoholism model.The global behavior of the model is investigated.It is proved that the system has a threshold dynamics in terms of the basic reproduction number(BRN),whe...We consider in this research an age-structured alcoholism model.The global behavior of the model is investigated.It is proved that the system has a threshold dynamics in terms of the basic reproduction number(BRN),where we obtained that alcohol-free equilibrium(AFE)is globally asymptotically stable(GAS)in the case R_(0)≤1,but for R_(0)>1 we found that the system persists and the nontrivial equilibrium(EE)is GAS.Furthermore,the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated,which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations.The obtained mathematical results are tested numerically next to its biological relevance.展开更多
In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transm...In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transmission is given.At last,some simulations are given to support our result.展开更多
A new mathematical model of chronic hepatitis C virus(HCV)infection incorporating humoral and cell-mediated immune responscs,distinct cell proliferation rates for both uninfected and infected hepatocytes,and antiviral...A new mathematical model of chronic hepatitis C virus(HCV)infection incorporating humoral and cell-mediated immune responscs,distinct cell proliferation rates for both uninfected and infected hepatocytes,and antiviral treatment all at once,is formulated and analyzed meticulously.Analysis of the model elucidates the existence of multiple equilibrium states.Moreover,the model has a locally asymptotically stable disease-free equilibrium(DFE)whenever the basic reproduction number is less than unity.Local sensitivity analysis(L.SA)result exhibits that the most influential(negatively sensitive)parameters on the epidemic threshold are the drug efficacy of blocking virus production and the drug efficacy of removing infection.However,LSA does not accurately assess uncertainty and scnsitivity in the system and may mislead us since by default this technique holds all other parameters fixed at baseline values.To overcome this pitfall,one of the most robust and efficient global sensitivity analysis(GSA)methods,which is Latin hypercube sampling-partial rank correlation coefficient technique,elucidates that the proliferation rate of infected hepatocytes and the drug efficacy of killing infected hep-atocytes are highly sensitive parameters that affect the transmission dynamics of HCV in any population.Our study suggests that cell proliferation of the infected hepatocytes can be very crucial in controlling disease outbreak.Thus,a future HCV drug that boosts cell-mediated immune response is expected to be quite effective in controlling disease outbreak.展开更多
This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons...This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.展开更多
In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach ...In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach each other from both sides of the x-axis, as t converge to-∞ and then converge to (1,0) as t converges to +∞. Its global dynamic shows the superior species invade the inferior ones from both sides of the x-axis and then the inferior ones become extinct, which is a new invading way. In fact, our conclusions extend this invading way into a more general competitive system. Furthermore, we show several properties of this entire solution.展开更多
In the present paper,an epidemic model with Z-type control mechanism has been pro- posed and analyzed to explore the disease control strategy on an infectious disease outbreak.The uncontrolled model can have a disease...In the present paper,an epidemic model with Z-type control mechanism has been pro- posed and analyzed to explore the disease control strategy on an infectious disease outbreak.The uncontrolled model can have a disease-free equilibrium and an endemic equilibrium.The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived.It is also observed that the disease-free equilibrium is globally asymptotically stable if R0<1,whereas the endemic equilibrium is globally asymptotically stable if R0>1.The model is further improved by considering Z-control mechanism and investigated.Disease can be controlled by using Z-control while the basic reproduction of the uncontrolled system is greater than unity.The positivity conditions of the solutions are derived and the basin of attraction for successful implementation of Z-control mechanism is also investigated.To verify the analytical findings,extensive numerical simulations on the model are carried out.展开更多
The stability of the predator-prey model subject to the Allee effect is an interesting topic in recent times.In this paper,we investigate the impact of weak Allee effect on the stability of a discrete-time predator-pr...The stability of the predator-prey model subject to the Allee effect is an interesting topic in recent times.In this paper,we investigate the impact of weak Allee effect on the stability of a discrete-time predator-prey model with Holling type-IV functional response.The mathematical features of the proposed model are analyzed with the help of equilibrium analysis,stability analysis,and bifurcation theory.We provide sufficient conditions for the flip bifurcation by considering Allee parameter as the bifurcation parameter.We observe that the model becomes stable from chaotic dynamics as the Allee parameter increases.Further,we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence equilibrium.Our analytical findings are illustrated through numerical simulations.展开更多
In this paper,Health-related quality of life has not been adequately measured in bladder cancer.A recently developed reliable and disease-specific quality of life instrument(Bladder Cancer Index,RCI)was used to measur...In this paper,Health-related quality of life has not been adequately measured in bladder cancer.A recently developed reliable and disease-specific quality of life instrument(Bladder Cancer Index,RCI)was used to measure.Progressive type Ⅱ censoring schemes have potential usefulness in practice where budget constraints in place or there is a necessity for the speedy test.To test the process capability,the lifetime performance index Cl is widely recommended for evaluating the performance of the producfs lifetime and evaluating the lifetime performance index GL for the three-parameter Weighted-Lomax distribution(WLx)under progressive type-II censoring sample for a lower specification limit(L).The statistical inference concerning CL is conducted via obtaining the maximum likelihood of Cl on the base of progressive type-II censoring.The asymptotic normal distribution of the MLE of CL and the confidence interval is proposed.Moreover,the hypothesis testing of CL for evaluating the lifetime performance of WLx data is conducted.Also,assuming the conjugate prior distribution and squared error loss function,this study constructs a Bayes estimator of CL.The Bayes estimator of CL is then utilized to develop a credible interval in the condition of known L.Moreover,we propose a Bayesian test to assess the lifetime performance of products.We also propose a Bayesian test to assess the lifetime performance of products.Finally,two examples are given,one of them is considering a real life data of the remission times of bladder cancer patients in endurance lifetime test and the other is a simulated example to illustrate the usage of the proposed procedure.展开更多
This paper presents a 2D simulation of transient heat transfer in the human eye using appropriate boundary conditions.The mathematical model governing bioheat transfer in the human eye is discussed and the existence a...This paper presents a 2D simulation of transient heat transfer in the human eye using appropriate boundary conditions.The mathematical model governing bioheat transfer in the human eye is discussed and the existence and uniqueness of the solution are proven.Four methods based on finite element method and nonoverlapping domain decomposition method to obtain transient heat transfer in the human eye are presented and described in details.After conducting numerous simulations using realistic parameters obtained from the open literature and after comparison with measurements reported by previous experimental studies,all proposed methods gave an accurate representation of transient heat transfer in the human eye.The results obtained by the domain decomposition of the human eye into four subdomains are found to be the closest to reality.展开更多
In this work,we have introduced an eco-epidemiological model of an infected predator prey system.Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption.Mor...In this work,we have introduced an eco-epidemiological model of an infected predator prey system.Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption.Moreover,to make the model more realistic to the environment,we have introduced strong Allee effect in the susceptible population.Boundedness and positivity of the solution have been established.Local stability conditions of the equilibrium points have been found with the help of Routh-Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease,then both the prey(susceptible and infected)and predator cannot survive simultaneously in the system for any parametric values.The disease transmission rate and the attack rate on the susceptible have an important role to control the system dynamics.For different values of these two key parameters,we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.展开更多
This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment.The influence of environmental fluctuation is accommodated ...This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment.The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable.Hence,a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints.With the help of maximum principle and the concept of blocked intervals,an optimal periodic solution has been obtained which is followed by the construe tion of optimal solution using the theory of most rapid approach.Important results of the study are demonstrated through numerical simulations.展开更多
Fractional-order gene regulatory networks with time delay(DFCIRNs)have proven that they are more suitable to model gene regulation mechanism than integer-order.In this paper,a novel DFGRN is proposed.The existence and...Fractional-order gene regulatory networks with time delay(DFCIRNs)have proven that they are more suitable to model gene regulation mechanism than integer-order.In this paper,a novel DFGRN is proposed.The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions.On this basis,the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN,and the stability conditions are dependent on the fractional-order q.Finally,numerical simulations show that the obtained results arc reasonable.展开更多
A two-sex deterministic model for Human Papillomavirus (HPV)that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigor- ously analyzed.The model is shown to exhibit the ph...A two-sex deterministic model for Human Papillomavirus (HPV)that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigor- ously analyzed.The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection,when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional,and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e.condom use and vaccination of both males and females).Numerical simulations of the model showed that,based on the parameter values used therein,a vaccine (with 75%efficacy)for male population with about 40%condom compliance by females will result in a significant reduction in the disease burden in the population.Also,the numerical simulations of the model reveal that with 70%condom compliance by the male population,administering female vaccine (with 45%efficacy)is sufficient for effective control of the disease.展开更多
基金Manjun Ma was supported by the National Natural Science Foundation of China(Nos.12071434 and 11671359).
文摘This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state,and show that the chemotactic flux is the key mechanism for pattern formation.Then,we treat the chemotaxis coefficient as a bifurcation parameter to obtain the asymptotic expressions of steady states.Based on this,we derive the sufficient conditions for the stability of one-step pattern,and prove the metastability of two or more step patterns.All the analytical results are demonstrated by numerical simulations.
基金supported by DGESTR of Algeria No.COOL03UN130120200004.
文摘We consider in this research an age-structured alcoholism model.The global behavior of the model is investigated.It is proved that the system has a threshold dynamics in terms of the basic reproduction number(BRN),where we obtained that alcohol-free equilibrium(AFE)is globally asymptotically stable(GAS)in the case R_(0)≤1,but for R_(0)>1 we found that the system persists and the nontrivial equilibrium(EE)is GAS.Furthermore,the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated,which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations.The obtained mathematical results are tested numerically next to its biological relevance.
文摘In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transmission is given.At last,some simulations are given to support our result.
文摘A new mathematical model of chronic hepatitis C virus(HCV)infection incorporating humoral and cell-mediated immune responscs,distinct cell proliferation rates for both uninfected and infected hepatocytes,and antiviral treatment all at once,is formulated and analyzed meticulously.Analysis of the model elucidates the existence of multiple equilibrium states.Moreover,the model has a locally asymptotically stable disease-free equilibrium(DFE)whenever the basic reproduction number is less than unity.Local sensitivity analysis(L.SA)result exhibits that the most influential(negatively sensitive)parameters on the epidemic threshold are the drug efficacy of blocking virus production and the drug efficacy of removing infection.However,LSA does not accurately assess uncertainty and scnsitivity in the system and may mislead us since by default this technique holds all other parameters fixed at baseline values.To overcome this pitfall,one of the most robust and efficient global sensitivity analysis(GSA)methods,which is Latin hypercube sampling-partial rank correlation coefficient technique,elucidates that the proliferation rate of infected hepatocytes and the drug efficacy of killing infected hep-atocytes are highly sensitive parameters that affect the transmission dynamics of HCV in any population.Our study suggests that cell proliferation of the infected hepatocytes can be very crucial in controlling disease outbreak.Thus,a future HCV drug that boosts cell-mediated immune response is expected to be quite effective in controlling disease outbreak.
基金supporting this work by the University Ajman Grant:2Q20-COVID-19-08.
文摘This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.
基金Y. Wang partially supported by the Natural Science Foundation of Shanxi Province (201801D221008)G. Liu partially supported by the NSFC (11471197)+2 种基金Natural Science Foundation of Shanxi Province (2014011005-1)X.Li partially supported by the NSFC (11571041)the Fundamental Research Funds for the Central Universities.
文摘In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach each other from both sides of the x-axis, as t converge to-∞ and then converge to (1,0) as t converges to +∞. Its global dynamic shows the superior species invade the inferior ones from both sides of the x-axis and then the inferior ones become extinct, which is a new invading way. In fact, our conclusions extend this invading way into a more general competitive system. Furthermore, we show several properties of this entire solution.
文摘In the present paper,an epidemic model with Z-type control mechanism has been pro- posed and analyzed to explore the disease control strategy on an infectious disease outbreak.The uncontrolled model can have a disease-free equilibrium and an endemic equilibrium.The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived.It is also observed that the disease-free equilibrium is globally asymptotically stable if R0<1,whereas the endemic equilibrium is globally asymptotically stable if R0>1.The model is further improved by considering Z-control mechanism and investigated.Disease can be controlled by using Z-control while the basic reproduction of the uncontrolled system is greater than unity.The positivity conditions of the solutions are derived and the basin of attraction for successful implementation of Z-control mechanism is also investigated.To verify the analytical findings,extensive numerical simulations on the model are carried out.
文摘The stability of the predator-prey model subject to the Allee effect is an interesting topic in recent times.In this paper,we investigate the impact of weak Allee effect on the stability of a discrete-time predator-prey model with Holling type-IV functional response.The mathematical features of the proposed model are analyzed with the help of equilibrium analysis,stability analysis,and bifurcation theory.We provide sufficient conditions for the flip bifurcation by considering Allee parameter as the bifurcation parameter.We observe that the model becomes stable from chaotic dynamics as the Allee parameter increases.Further,we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence equilibrium.Our analytical findings are illustrated through numerical simulations.
文摘In this paper,Health-related quality of life has not been adequately measured in bladder cancer.A recently developed reliable and disease-specific quality of life instrument(Bladder Cancer Index,RCI)was used to measure.Progressive type Ⅱ censoring schemes have potential usefulness in practice where budget constraints in place or there is a necessity for the speedy test.To test the process capability,the lifetime performance index Cl is widely recommended for evaluating the performance of the producfs lifetime and evaluating the lifetime performance index GL for the three-parameter Weighted-Lomax distribution(WLx)under progressive type-II censoring sample for a lower specification limit(L).The statistical inference concerning CL is conducted via obtaining the maximum likelihood of Cl on the base of progressive type-II censoring.The asymptotic normal distribution of the MLE of CL and the confidence interval is proposed.Moreover,the hypothesis testing of CL for evaluating the lifetime performance of WLx data is conducted.Also,assuming the conjugate prior distribution and squared error loss function,this study constructs a Bayes estimator of CL.The Bayes estimator of CL is then utilized to develop a credible interval in the condition of known L.Moreover,we propose a Bayesian test to assess the lifetime performance of products.We also propose a Bayesian test to assess the lifetime performance of products.Finally,two examples are given,one of them is considering a real life data of the remission times of bladder cancer patients in endurance lifetime test and the other is a simulated example to illustrate the usage of the proposed procedure.
文摘This paper presents a 2D simulation of transient heat transfer in the human eye using appropriate boundary conditions.The mathematical model governing bioheat transfer in the human eye is discussed and the existence and uniqueness of the solution are proven.Four methods based on finite element method and nonoverlapping domain decomposition method to obtain transient heat transfer in the human eye are presented and described in details.After conducting numerous simulations using realistic parameters obtained from the open literature and after comparison with measurements reported by previous experimental studies,all proposed methods gave an accurate representation of transient heat transfer in the human eye.The results obtained by the domain decomposition of the human eye into four subdomains are found to be the closest to reality.
文摘In this work,we have introduced an eco-epidemiological model of an infected predator prey system.Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption.Moreover,to make the model more realistic to the environment,we have introduced strong Allee effect in the susceptible population.Boundedness and positivity of the solution have been established.Local stability conditions of the equilibrium points have been found with the help of Routh-Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease,then both the prey(susceptible and infected)and predator cannot survive simultaneously in the system for any parametric values.The disease transmission rate and the attack rate on the susceptible have an important role to control the system dynamics.For different values of these two key parameters,we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.
文摘This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment.The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable.Hence,a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints.With the help of maximum principle and the concept of blocked intervals,an optimal periodic solution has been obtained which is followed by the construe tion of optimal solution using the theory of most rapid approach.Important results of the study are demonstrated through numerical simulations.
基金the Hunan Provincial Natural Science Foundation(No.2019JJ50222)the Hunan Province Science and Technology Project(No.2015JC3101)also by the Scientific Research Fund of Hunan Provincial Education Department(No.14B090).
文摘Fractional-order gene regulatory networks with time delay(DFCIRNs)have proven that they are more suitable to model gene regulation mechanism than integer-order.In this paper,a novel DFGRN is proposed.The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions.On this basis,the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN,and the stability conditions are dependent on the fractional-order q.Finally,numerical simulations show that the obtained results arc reasonable.
文摘A two-sex deterministic model for Human Papillomavirus (HPV)that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigor- ously analyzed.The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection,when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional,and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e.condom use and vaccination of both males and females).Numerical simulations of the model showed that,based on the parameter values used therein,a vaccine (with 75%efficacy)for male population with about 40%condom compliance by females will result in a significant reduction in the disease burden in the population.Also,the numerical simulations of the model reveal that with 70%condom compliance by the male population,administering female vaccine (with 45%efficacy)is sufficient for effective control of the disease.
