The purpose of this paper is to study the singular values and real fixed points of one parameter family of function,fλ（z）=λab2/b2-1,fλ（0）=λ/lnb for λ∈R／{0},z∈C and b〉 0 except b = 1. It is found that the ...The purpose of this paper is to study the singular values and real fixed points of one parameter family of function,fλ（z）=λab2/b2-1,fλ（0）=λ/lnb for λ∈R／{0},z∈C and b〉 0 except b = 1. It is found that the function fλ（z） has infinitely many singular values for all b 〉 0 except b = 1. It is also shown that, for 0 〈 b 〈 1, all the critical values of fλ（z） lie in the left half plane while, for b 〉 1, lie in the right half plane. Further, it is seen that all these critical values are outside the open disk centered at origin and having radius ｜λ/lnb｜for all b 〉 0 except b = 1. Moreover, the real fixed points of fλ （z） and their nature are investigated.展开更多
In this paper,we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus(COVID-19).The model incorporates the effect of transmission and treatment on the occurrence of new infe...In this paper,we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus(COVID-19).The model incorporates the effect of transmission and treatment on the occurrence of new infections.For the model,the basic reproduction number(R_(0))has been computed.Corresponding to the threshold quantity(R_(0)),the stability of endemic and disease-free equilibrium(DFE)points are determined.For R_(0)>1,if the endemic equilibrium point exists,then it is locally asymptotically stable,whereas the DFE point is globally asymptotically stable for R_(0)<1 which implies the eradication of the disease.The effects of various parameters on the spread of COVID-19 are discussed in the segment of sensitivity analysis.The model is numerically simulated to understand the effect of reproduction number on the transmission dynamics of the disease COVID-19.From the numerical simulations,it is concluded that if the reproduction number for the coronavirus disease is reduced below unity by decreasing the transmission rate and detecting more number of infectives,then the epidemic can be eradicated from the population.展开更多
文摘The purpose of this paper is to study the singular values and real fixed points of one parameter family of function,fλ（z）=λab2/b2-1,fλ（0）=λ/lnb for λ∈R／{0},z∈C and b〉 0 except b = 1. It is found that the function fλ（z） has infinitely many singular values for all b 〉 0 except b = 1. It is also shown that, for 0 〈 b 〈 1, all the critical values of fλ（z） lie in the left half plane while, for b 〉 1, lie in the right half plane. Further, it is seen that all these critical values are outside the open disk centered at origin and having radius ｜λ/lnb｜for all b 〉 0 except b = 1. Moreover, the real fixed points of fλ （z） and their nature are investigated.
文摘In this paper,we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus(COVID-19).The model incorporates the effect of transmission and treatment on the occurrence of new infections.For the model,the basic reproduction number(R_(0))has been computed.Corresponding to the threshold quantity(R_(0)),the stability of endemic and disease-free equilibrium(DFE)points are determined.For R_(0)>1,if the endemic equilibrium point exists,then it is locally asymptotically stable,whereas the DFE point is globally asymptotically stable for R_(0)<1 which implies the eradication of the disease.The effects of various parameters on the spread of COVID-19 are discussed in the segment of sensitivity analysis.The model is numerically simulated to understand the effect of reproduction number on the transmission dynamics of the disease COVID-19.From the numerical simulations,it is concluded that if the reproduction number for the coronavirus disease is reduced below unity by decreasing the transmission rate and detecting more number of infectives,then the epidemic can be eradicated from the population.
