In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.

We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD) heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to(x-)-1/2wherex-is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.

Rift Valley fever (RVF) outbreaks are recurrent, occurring at irregular intervals of up to 15 years at least in East Africa. Between outbreaks disease inter-epidemic activities exist and occur at low levels and are maintained by female Aedes mcintoshi mosquitoes which transmit the virus to their eggs leading to disease persistence during unfavourable seasons. Here we formulate and analyse a full stochastic host-vector model with two routes of transmission: vertical and horizontal. By applying branching process theory we establish novel relationships between the basic reproduction number, R₀, vertical transmission and the invasion and extinction probabilities. Optimum climatic conditions and presence of mosquitoes have not fully explained the irregular oscillatory behaviour of RVF outbreaks. Using our model without seasonality and applying van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how outbreaks multi-year periodicity varies with the vertical transmission. Our theory predicts complex fluctuations with a dominant period of 1 to 10 years which essentially depends on the efficiency of vertical transmission. Our predictions are then compared to temporal patterns of disease outbreaks in Tanzania, Kenya and South Africa. Our analyses show that interaction between nonlinearity, stochasticity and vertical transmission provides a simple but plausible explanation for the irregular oscillatory nature of RVF outbreaks. Therefore, we argue that while rainfall might be the major determinant for the onset and switch-off of an outbreak, the occurrence of a particular outbreak is also a result of a build up phenomena that is correlated to vertical transmission efficiency. Rift Valley fever (RVF) is a relatively novel vector-borne zoonotic disease, with long and irregular periods between outbreaks. Although outbreaks are highly correlated with occurrence of abnormal rainfall and flooding regimes, there have been instances with above normal rainfall where no disease outbreaks were recorded. This suggests that while rainfall might be the major determinant for the onset and switch-off of an outbreak, it may not be the only factor responsible for the temporal characteristic pattern of RVF outbreaks. We suspect that apart from influence of environmental conditions, disease outbreaks result from build up phenomena that depend on vertical transmission efficiency. Therefore, in this study we focus on formulating a stochastic host-vector model with two routes of transmission (horizontal and vertical) without seasonality to investigate the role of vertical transmission in the dynamics of the disease. First we apply branching process theory to characterize the relationships between vertical transmission and invasion probability and between vertical transmission and extinction probability. Finally, we apply an analytic approach, van Kampen’s system size expansion method to characterize disease complex fluctuations that are simply a result of interaction between demographic stochasticity, non-linearity and vertical transmission efficiency. Our results show that it is possible to reduce the frequency and intensity of RVF outbreaks by simply reducing the efficiency of vertical transmission.

Lymphatic filariasis is a globally neglected tropical parasitic disease which affects individuals of all ages and leads to an altered lymphatic system and abnormal enlargement of body parts. A mathematical model of lymphatic filariaris with intervention strategies is developed and analyzed. Control of infections is analyzed within the model through medical treatment of infected-acute individuals and quarantine of infected-chronic individuals. We derive the effective reproduction number, $\mathcal {R}_{0},$ and its interpretation/investigation suggests that treatment contributes to a reduction in lymphatic filariasis cases faster than quarantine. However, this reduction is greater when the two intervention approaches are applied concurrently. Numerical simulations are carried out to monitor the dynamics of the filariasis model sub-populations for various parameter values of the associated reproduction threshold. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance on the disease transmission.

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number.