Some qualitative properties of the discrete models for malaria propagation

• This paper analyzes a seven-dimensional system of ODEs as model malaria propagation and seeks qualitative properties the on numerical levels so-called dynamical consistency. The is solved by nonstandard θ -method including nonlocal scheme standard to right side step-size function approximate time derivatives with first-order consistency valid for any step size. addresses reliable mathematical modeling in infected societies humans mosquitoes an extension basic Ross–Macdonald model. We analyze extended Ross numerically which initial value problem ODEs. For this aim, discretized split into two parts. First, we apply functions Then use discretization obtain linear system. find conditions under specific intervals are positively invariant total populations each component solution suggest preserve size Δ t . simulations confirm theoretical results examples compare efficiency Runge–Kutta methods different sufficiently large sizes.