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.

In this paper, we obtain approximate bound state solutions of an N-dimensional fractional time independent Schrödinger equation for a generalised Mie-type potential, namely, $V\left(r^{\alpha }\right)=\frac{A}{r^{2\alpha }}+\frac{B}{r^{\alpha }}+C$ . Here α(0 < α < 1) acts like a fractional parameter for the space variable r. When α = 1 the potential converts into the original form of Mie-type of potential that is generally studied in molecular and chemical physics. The entire study is composed with a Jumarie-type fractional derivative approach. The solution is expressed via the Mittag-Leffler function and fractionally defined confluent hypergeometric function. To ensure the validity of the present work, obtained results are verified with the previous studies for different potential parameter configurations, specially for α = 1. At the end, few numerical calculations for energy eigenvalue and bound state eigenfunctions are furnished for a typical diatomic molecule.

Bump-on-tail instability of Langmuir waves propagating in unmagnetized Lorentzian plasma modeled by a Kappa velocity distribution with spectral index κ has been investigated in this paper. Growth rate of this microinstability has been determined analytically from the Langmuir wave dispersion relation. Change in the maximum growth rate with increasing κ has been numerically estimated for different number density and temperature ratios using solar wind data.

In this paper the effect of secondary electron emission on Jeans instability in a dusty plasma has been investigated. Due to secondary electron emission, dust grains may have two stable equilibrium states out of which one is negative and the other is positive. Here both cases have been considered separately. It has been shown that secondary electron emission enhances Jeans instability when equilibrium dust charge is negative. It has also been shown that growth rate of Jeans instability reduces with increasing secondary electron emission when equilibrium dust charge is positive.