In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equa- ti...In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equa- tions. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge- Kutta method which supports the theoretical findings. It is found that both infected and uninfected tumor cells and hence tumor load can be eliminated with time, and complete recovery is possible because of virus therapy, if certain conditions are satisfied. It is further found that the system appears to exhibit periodic limit cycles and chaotic attractors for some ranges of the system parameters.展开更多
The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrializatio...The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We find out the critical value of delay and observe that there is Hopf bifurcation. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations are given to illustrate the analytical results.展开更多
In this paper,we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae(immature)stage.Both the Mosquito and human populations are divided into su...In this paper,we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae(immature)stage.Both the Mosquito and human populations are divided into susceptible and infective class.Sus-ceptible class of mosquito population is further divided into mature and immature.The model is analyzed by using stability theory of nonlinear ordinary differential equations.Basic reproduction ratio is derived which is found to be the decreasing function of maturation delay and larvicidal activity.In addition,it is observed that biting rate of mosquito,transmission efficiency of parasitic infection from infective human to mosquito and critical value of maturation delay are the key parameters determining the stability switch in the system.Numerical simulation is also carried out to confirm the analytical results obtained in the paper.展开更多
In this paper,a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource.It is assumed th...In this paper,a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource.It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass.Further,it is assumed that the resource biomass too is growing logistically in the envi-ronment and its carrying capacity decreases with the increase in densities of competing species and industrialization.The growth rate of population pressure is assumed to be proportional to the densities of competing species.Stabilities of all equilibria and con-ditions which influence the permanence of the system are carried out using theory of differential equations.Numerical simulations are performed to accomplish our analytical findings.It is shown that the equilibrium density of resource biomass decreases as(i)the growth rate coefficient of population pressure increases(ii)the growth rate coeffi-cient of industrialization due to population pressure increases and(iii)the growth rate coefficient of industrialization due to resource biomass increases.It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure.Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.展开更多
The present paper demonstrates the applicability of finite element method of weighted residuals to study the effects of precipitation scavenging through raindrops on the steady-state dispersion of air pollutants in th...The present paper demonstrates the applicability of finite element method of weighted residuals to study the effects of precipitation scavenging through raindrops on the steady-state dispersion of air pollutants in the atmosphere under realistic variable wind and diffusivity profiles.Here,the washout of pollutants by rain droplets is considered and the whole analysis for the pollutant concentration is carried out in two phases viz.gaseous phase and droplet phase.The model solutions are obtained by using local basis and asymmetric quadratic weighting functions which can provide a promising alternative to the standard Galerkin formulation for problems with advective and diffusive terms.The results of the model reveal that the precipitation scavenging by rain is quite effective in cleaning the polluted atmosphere.Anticipating the need of pollutant concentration in rain drops regarding acid precipitation(or acid rain),the concentration of the absorbed pollutant in the droplet phase are also analyzed.So,the present study provides an understanding on the concentration distribution of pollutant in gaseous and droplet phases,under the effects of variable wind and diffusivity profiles.展开更多
文摘In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equa- tions. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge- Kutta method which supports the theoretical findings. It is found that both infected and uninfected tumor cells and hence tumor load can be eliminated with time, and complete recovery is possible because of virus therapy, if certain conditions are satisfied. It is further found that the system appears to exhibit periodic limit cycles and chaotic attractors for some ranges of the system parameters.
文摘The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We find out the critical value of delay and observe that there is Hopf bifurcation. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations are given to illustrate the analytical results.
文摘In this paper,we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae(immature)stage.Both the Mosquito and human populations are divided into susceptible and infective class.Sus-ceptible class of mosquito population is further divided into mature and immature.The model is analyzed by using stability theory of nonlinear ordinary differential equations.Basic reproduction ratio is derived which is found to be the decreasing function of maturation delay and larvicidal activity.In addition,it is observed that biting rate of mosquito,transmission efficiency of parasitic infection from infective human to mosquito and critical value of maturation delay are the key parameters determining the stability switch in the system.Numerical simulation is also carried out to confirm the analytical results obtained in the paper.
文摘In this paper,a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource.It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass.Further,it is assumed that the resource biomass too is growing logistically in the envi-ronment and its carrying capacity decreases with the increase in densities of competing species and industrialization.The growth rate of population pressure is assumed to be proportional to the densities of competing species.Stabilities of all equilibria and con-ditions which influence the permanence of the system are carried out using theory of differential equations.Numerical simulations are performed to accomplish our analytical findings.It is shown that the equilibrium density of resource biomass decreases as(i)the growth rate coefficient of population pressure increases(ii)the growth rate coeffi-cient of industrialization due to population pressure increases and(iii)the growth rate coefficient of industrialization due to resource biomass increases.It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure.Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.
文摘The present paper demonstrates the applicability of finite element method of weighted residuals to study the effects of precipitation scavenging through raindrops on the steady-state dispersion of air pollutants in the atmosphere under realistic variable wind and diffusivity profiles.Here,the washout of pollutants by rain droplets is considered and the whole analysis for the pollutant concentration is carried out in two phases viz.gaseous phase and droplet phase.The model solutions are obtained by using local basis and asymmetric quadratic weighting functions which can provide a promising alternative to the standard Galerkin formulation for problems with advective and diffusive terms.The results of the model reveal that the precipitation scavenging by rain is quite effective in cleaning the polluted atmosphere.Anticipating the need of pollutant concentration in rain drops regarding acid precipitation(or acid rain),the concentration of the absorbed pollutant in the droplet phase are also analyzed.So,the present study provides an understanding on the concentration distribution of pollutant in gaseous and droplet phases,under the effects of variable wind and diffusivity profiles.
