Background:Schistosomiasis is a parasitic disease.It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites.Schistosomiasis is the second most parasiti...Background:Schistosomiasis is a parasitic disease.It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites.Schistosomiasis is the second most parasitic disease globally,so investigating its prevention and treatment is crucial.Methods:This paper aims to suggest a time-fractional model of schistosomiasis disease(T-FMSD)in the sense of the Caputo operator.The T-FMSD considers the dynamics involving susceptible ones not infected with schistosomiasis(S_(h)(t)),those infected with the infection(Ih(t)),those recovering from the disease(R(t)),susceptible snails with and without schistosomiasis infection,respectively shown by I_(v)(t)and S_(v)(t).We use a new basis function,generalized Bernoulli polynomials,for the approximate solution of T-FMSD.The operational matrices are incorporated into the method of Lagrange multipliers so that the fractional problem can be transformed into an algebraic system of equations.Results:The existence and uniqueness of the solution,and the convergence analysis of the model are established.The numerical computations are graphically presented to depict the variations of the compartments with time for varied fractional order derivatives.Conclusions:The proposed method not only provides an accurate solution but also can accurately predict schistosomiasis transmission.The results of this study will assist medical scientists in taking necessary measures during screening and treatment processes.展开更多
The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a cryst...The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a crystal lattice.This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation(FFKdVE)under gH-differentiability of Caputo fractional order,namely the q-Homotopy analysis method with the Shehu transform(q-HASTM).A triangular fuzzy number describes the Caputo fractional derivative of orderα,0<α≤1,for modelling problem.The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are in-vestigated using a robust double parametric form-based q-HASTM with its convergence analysis.The ob-tained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.展开更多
This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma physics.The solution of the G...This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma physics.The solution of the GPE is approximated via the finite difference technique and the localized meshless radial basis function generated finite difference.The association of the technique results in a meshless approach that does not require linearizing the nonlinear terms.At the first step,the PDE is converted to a system of nonlinear ODEs with the help of the radial kernels.In the second step,a high-order ODE solver is adopted to discretize the nonlinear ODE system.The global collocation techniques pose a considerable computationl burden due to the calculation of the dense algebraic system.The proposed method approx-imates differential operators over the local support domain,leading to sparse differentiation matrices and decreasing the computational burden.Numerical results and comparisons are provided to confirm the efficiency and accuracy of the method.展开更多
This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically,and numerically.The analytical results are obtained usi...This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically,and numerically.The analytical results are obtained using thenormal form technique and numerical results are obtained using the numerical continuation method.For this model,a number of bifurcations are studied,including the transcritical(pitchfork)and fip bifurcations,the Neimark-Sacker(NS)bifurcations,and the strong resonance bifurcations.We especially determine the dynamical behaviors of the model for higher iterations up to fourth-order.Numerical simulation is employed to present a closed invariant curve emerging about an NS point,and its breaking down to several closed invariant curves and eventuality giving rise to a chaotic strange attractor by increasing the bifurcation parameter.展开更多
This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-curr...This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the reservoir.For different fractional orders in both porous matrix and fractured porous media,the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery rates.Finally,the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.展开更多
文摘Background:Schistosomiasis is a parasitic disease.It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites.Schistosomiasis is the second most parasitic disease globally,so investigating its prevention and treatment is crucial.Methods:This paper aims to suggest a time-fractional model of schistosomiasis disease(T-FMSD)in the sense of the Caputo operator.The T-FMSD considers the dynamics involving susceptible ones not infected with schistosomiasis(S_(h)(t)),those infected with the infection(Ih(t)),those recovering from the disease(R(t)),susceptible snails with and without schistosomiasis infection,respectively shown by I_(v)(t)and S_(v)(t).We use a new basis function,generalized Bernoulli polynomials,for the approximate solution of T-FMSD.The operational matrices are incorporated into the method of Lagrange multipliers so that the fractional problem can be transformed into an algebraic system of equations.Results:The existence and uniqueness of the solution,and the convergence analysis of the model are established.The numerical computations are graphically presented to depict the variations of the compartments with time for varied fractional order derivatives.Conclusions:The proposed method not only provides an accurate solution but also can accurately predict schistosomiasis transmission.The results of this study will assist medical scientists in taking necessary measures during screening and treatment processes.
文摘The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a crystal lattice.This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation(FFKdVE)under gH-differentiability of Caputo fractional order,namely the q-Homotopy analysis method with the Shehu transform(q-HASTM).A triangular fuzzy number describes the Caputo fractional derivative of orderα,0<α≤1,for modelling problem.The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are in-vestigated using a robust double parametric form-based q-HASTM with its convergence analysis.The ob-tained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.
文摘This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma physics.The solution of the GPE is approximated via the finite difference technique and the localized meshless radial basis function generated finite difference.The association of the technique results in a meshless approach that does not require linearizing the nonlinear terms.At the first step,the PDE is converted to a system of nonlinear ODEs with the help of the radial kernels.In the second step,a high-order ODE solver is adopted to discretize the nonlinear ODE system.The global collocation techniques pose a considerable computationl burden due to the calculation of the dense algebraic system.The proposed method approx-imates differential operators over the local support domain,leading to sparse differentiation matrices and decreasing the computational burden.Numerical results and comparisons are provided to confirm the efficiency and accuracy of the method.
文摘This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically,and numerically.The analytical results are obtained using thenormal form technique and numerical results are obtained using the numerical continuation method.For this model,a number of bifurcations are studied,including the transcritical(pitchfork)and fip bifurcations,the Neimark-Sacker(NS)bifurcations,and the strong resonance bifurcations.We especially determine the dynamical behaviors of the model for higher iterations up to fourth-order.Numerical simulation is employed to present a closed invariant curve emerging about an NS point,and its breaking down to several closed invariant curves and eventuality giving rise to a chaotic strange attractor by increasing the bifurcation parameter.
文摘This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous media.The correlation be-tween the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the reservoir.For different fractional orders in both porous matrix and fractured porous media,the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery rates.Finally,the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.
