Browsing by Author "Jawaz, Muhammad"

Now showing 1 - 2 of 2

Citation - WoS: 4
Citation - Scopus: 3
Analysis and Numerical Effects of Time-Delayed Rabies Epidemic Model With Diffusion
(Walter de Gruyter Gmbh, 2023) Rehman, Muhammad Aziz-Ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; Jawaz, Muhammad
The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von-Neumann method. Taylor's expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of tau on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.
Citation - WoS: 8
Citation - Scopus: 8
Numerical and Bifurcation Analysis of Spatio-Temporal Delay Epidemic Model
(Elsevier, 2021) Rehman, Muhammad Aziz Ur; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Jawaz, Muhammad; ur Rehman, Muhammad Aziz
HIV/AIDS is a distressing and incurable disease of the human beings. In this article, we have proposed a numerical structure for the HIV/AIDS compartmental model with diffusion and delay process. The proposed scheme has the proficiency to preserve the positivity of the state variables. Also, the proposed scheme leads to the consistency and stability. Two equilibrium states of the model have been described. Moreover, the stability of the scheme is examined at these two states. The contribution of the basic reproductive number R-0, in stability analysis is also investigated. The bifurcation value of the infection parameter gamma, for different situations of tau is also investigated. Graphical solutions with the aid of computer simulations are presented to clarify the paramount features of the proposed numerical design.