The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonome...The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization.展开更多
In this paper,we have developed and analyzed a deterministic Zika model considering both vector and sexual transmission route with the effect of human awareness and vector control in the absence of disease induce deat...In this paper,we have developed and analyzed a deterministic Zika model considering both vector and sexual transmission route with the effect of human awareness and vector control in the absence of disease induce death.To formulate the model,we assume that the Zika virus is being first transmitted to human by mosquito bite,and then it is being transmitted to his or her sexual partner.The system contains at most three equilibrium points among them one is the disease free and other two are endemic equilibrium points,exists under certain conditions.The theoretical analysis shows that the diseases-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one.Theatrically we have established that endemic equilibrium point which is locally asymptotically stable if the basic reproduction number is greater than one.The system exhibits backward bifurcation when the transmission probability per biting of susceptible mosquito with infected humans crosses the critical value.We estimate the model parameters and validate the model by fitting the model with the reported Zika infected human data from 1 to 36 week of 2016 Zika outbreak in Colombia.Furthermore,using the normalised forward sensitivity index method we have established that the model parameter mosquito biting rate,recruitment rate of mosquito,transmission probability per biting of Susceptible(infected)humans with infected(susceptible)mosquito,rate of awareness in host population,recovery rates of infected human are most sensitive parameters of the considered Zika model.Lastly,some conclusions are given to control the spreading of the Zika disease.展开更多
基金Board of Research in Nuclear Science (BRNS), Department of Atomic Energy Government of India
文摘The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization.
文摘In this paper,we have developed and analyzed a deterministic Zika model considering both vector and sexual transmission route with the effect of human awareness and vector control in the absence of disease induce death.To formulate the model,we assume that the Zika virus is being first transmitted to human by mosquito bite,and then it is being transmitted to his or her sexual partner.The system contains at most three equilibrium points among them one is the disease free and other two are endemic equilibrium points,exists under certain conditions.The theoretical analysis shows that the diseases-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one.Theatrically we have established that endemic equilibrium point which is locally asymptotically stable if the basic reproduction number is greater than one.The system exhibits backward bifurcation when the transmission probability per biting of susceptible mosquito with infected humans crosses the critical value.We estimate the model parameters and validate the model by fitting the model with the reported Zika infected human data from 1 to 36 week of 2016 Zika outbreak in Colombia.Furthermore,using the normalised forward sensitivity index method we have established that the model parameter mosquito biting rate,recruitment rate of mosquito,transmission probability per biting of Susceptible(infected)humans with infected(susceptible)mosquito,rate of awareness in host population,recovery rates of infected human are most sensitive parameters of the considered Zika model.Lastly,some conclusions are given to control the spreading of the Zika disease.
