TY  - JOUR
AU  - Younas, Hazrat
AU  - Ahmad, Imtiaz
AU  - Ullah, Zakir
AU  - Ullah, Hanif
PY  - 2026
DA  - 2026/04/15
TI  - Mathematical Modeling of Rabies Control: Evaluating Vaccination Strategies via NSFD and RK4 Approaches
JO  - Journal of Numerical Simulations in Physics and Mathematics
T2  - Journal of Numerical Simulations in Physics and Mathematics
JF  - Journal of Numerical Simulations in Physics and Mathematics
VL  - 2
IS  - 1
SP  - 9
EP  - 24
DO  - 10.62762/JNSPM.2026.413156
UR  - https://www.icck.org/article/abs/JNSPM.2026.413156
KW  - rabies
KW  - stability analysis
KW  - RK4 versus the NSFD method
AB  - The initial mathematical model for rabies consists of six compartments representing the human and dog populations: $S_h, I_h, V_h, S_d, I_d, V_d$. To obtain a more realistic description of rabies transmission dynamics, we extend the model by introducing two additional human compartments: Exposed ($E_h$) and Recovered ($R_h$) individuals. The extended system therefore comprises eight compartments: $S_h, E_h, I_h, V_h, R_h, S_d, I_d, V_d$. This extension captures important differences in disease progression, treatment response, and transmission pathways. Within this framework, we examine the positivity and boundedness of solutions, derive the basic reproduction number ($R_0$), analyse the sensitivity of $R_0$ to key epidemiological parameters, and investigate the global stability of the endemic equilibrium. Numerical simulations are carried out using both the classical fourth-order Runge-Kutta (RK4) method and the Nonstandard Finite Difference (NSFD) method, allowing us to compare their accuracy and reliability in predicting population dynamics.
SN  - 3068-9082
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Younas2026Mathematic,
  author = {Hazrat Younas and Imtiaz Ahmad and Zakir Ullah and Hanif Ullah},
  title = {Mathematical Modeling of Rabies Control: Evaluating Vaccination Strategies via NSFD and RK4 Approaches},
  journal = {Journal of Numerical Simulations in Physics and Mathematics},
  year = {2026},
  volume = {2},
  number = {1},
  pages = {9-24},
  doi = {10.62762/JNSPM.2026.413156},
  url = {https://www.icck.org/article/abs/JNSPM.2026.413156},
  abstract = {The initial mathematical model for rabies consists of six compartments representing the human and dog populations: \$S\_h, I\_h, V\_h, S\_d, I\_d, V\_d\$. To obtain a more realistic description of rabies transmission dynamics, we extend the model by introducing two additional human compartments: Exposed (\$E\_h\$) and Recovered (\$R\_h\$) individuals. The extended system therefore comprises eight compartments: \$S\_h, E\_h, I\_h, V\_h, R\_h, S\_d, I\_d, V\_d\$. This extension captures important differences in disease progression, treatment response, and transmission pathways. Within this framework, we examine the positivity and boundedness of solutions, derive the basic reproduction number (\$R\_0\$), analyse the sensitivity of \$R\_0\$ to key epidemiological parameters, and investigate the global stability of the endemic equilibrium. Numerical simulations are carried out using both the classical fourth-order Runge-Kutta (RK4) method and the Nonstandard Finite Difference (NSFD) method, allowing us to compare their accuracy and reliability in predicting population dynamics.},
  keywords = {rabies, stability analysis, RK4 versus the NSFD method},
  issn = {3068-9082},
  publisher = {Institute of Central Computation and Knowledge}
}