ABSTRACT
Dengue fever epidemic is an important infectious disease causing significant casualties and socioeconomic losses around the globe. There is an enormous pressure on public health policy makers for deriving standard guidelines and making effective decisions to safeguard the public from the dengue hazards. Mathematical modeling of dengue disease helps the decision-makers in understanding the disease dynamics and halting its spreading. This work introduces an innovative evolutionary computing and Padѐ rational approximation-based hybrid meshfree approach for analyzing the dynamical diffusion of dengue fever disease involving incubation epoch of virus. The proposed framework employs Padѐ approximation, penalty function approach, Nelder–Mead simplex (NMS) algorithm, and differential evolution (DE) to model and solve an equivalent optimization problem. The resulting method is named as differential cooperative multi-simplex Padѐ approximation (DCMP) scheme. The underlying dynamical model is analyzed for stabilities of its steady states. It is also shown that the proposed DCMP scheme possesses fast unconditional convergence, and preserves boundedness and positivity of the solution. Unlike the Euler (EU) and fourth-order Runge–Kutta (RK4) methods, the developed DCMP scheme is independent of discretization step length. The comparisons of results of DCMP with nonstandard finite difference scheme (NSFD) conform that the proposed DCMP truly exhibits the dynamics of the considered dengue disease model, involving incubation period of virus.
