Asad Ullah

The World Health Organization (WHO) constantly reports outbreaks of dengue, mostly in different countries of tropical and subtropical regions. The most alarming effect of dengue is that there is no specific medical treatment for this sessional disease. Delaying the transmission of dengue is one of anticipation. So, in this continuation paper, first, we presented the previously missing dynamical analysis of the deterministic dengue system, including positivity, boundedness, and asymptotic behavior of system convergence around the consequent equilibrium states. Parameter sensitivity concerning the reproductive number is investigated and graphically explained. Derivation of the stochastic delayed dengue model by the non-parametric perturbation technique is presented and its global positivity is investigated. The proposed non-standard finite difference theoretical and continuous analysis is presented. First, the sensitivity of model parameters about the reproductive number is explained and simulated. Second, we discuss whether the numerical analysis of the previously discussed schemes for the stochastic dengue model also effectively functions for the stochastic delayed dengue mathematical model. Finally, the classical impact of delayed tactics on the stochastic delayed model and reproductive number is explained rigorously.