Modelling the impact of some control strategies on the transmission dynamics of Ebola virus in human-bat population: An optimal control analysis.

Qualitative research and comprehensive public awareness to nip the transmission of Ebola virus in the bud before it becomes a global threat is fast becoming imperative especially now that the Gambia Ebola virus is mutated. It is therefore necessary to consider and investigate a vector-host transmission model for possible control strategy of this deadly disease. Hence, in this study, we presented a novel and feasible human-bat (host-vector) model which foretells the spread and severity of the Ebola virus from bats to humans to investigate the combined effects of three control strategies viz: (1) allowing specialized and designated agencies to bury deceased from Ebola infection without relatives touching or curdling the remains as usually practiced in most part of Africa as last respect for their departed love ones ( ), (2) systematic and deliberate depopulation of bats in the metropolis (through persecution with pesticide exposure, pre capturing, chemical timber treatment for roosts destruction) to discourage hunting them for food by virtue of their proximity ( ) and (3) immediate treatment of infected individuals in isolation ( ).

Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics.

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour.

A solitary wave solution to the generalized Burgers-Fisher's equation using an improved differential transform method: A hybrid scheme approach.

In this research, an unrivalled hybrid scheme which involves the coupling of the new Elzaki integral transform (an improved version of Laplace transform) and a modified differential transform called the projected differential transform (PDTM) have been implemented to solve the generalized Burgers-Fisher's equation; which springs up due to the fusion of the Burgers' and the Fisher's equation; describing convective effects, diffusion transport or interaction between reaction mechanisms, traffic flows; and turbulence; consequently finding meaningful applicability in the applied sciences viz: gas dynamics, fluid dynamics, turbulence theory, reaction-diffusion theory, shock-wave formation, traffic flows, financial mathematics, and so on. Using the proposed Elzaki projected differential transform method (EPDTM), a generalized exact solution (Solitary solution) in form of a Taylor multivariate series has been obtained; of which the highly nonlinear terms and derivatives handled by PDTM have been decomposed without expansion, computation of Adomian or He's polynomials, discretization, restriction of parameters, and with less computational work whilst achieving a highly convergent results when compared to other existing analytical/exact methods in the literature, via comparison tables, 3D plots, convergence plots and fluid-like plots. Thus showing the distinction, novelty and huge advantage of the proposed method as an asymptotic alternative, in providing generalized or solitary wave solution to a wider class of differential equations.