# Modeling Rabies Dynamics: The Impact of Vaccination and Infectious Immigrants on Public Health

## Authors

• Hazrat Younas Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
• Imtiaz Ahmad Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
• Nigar Ali Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
• Ihtisham Ul Haq Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
• Mohammed Daher Albalwi Yanbu Industrial College, The Royal Commission for Jubail and Yanbu, 30436, Saudi Arabia
• Shah Muhammad Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
• Mohammad Shuaib Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India

## Keywords:

SEV IR mathematical model, rabies, stability analysis, bifurcation, numerical simulation

## Abstract

Public health is still seriously threatened by rabies in many parts of the world, particularly in poorer nations. In order to address this issue, this work suggests an equation describing the mechanisms of rabies transmission between animals, taking into account infectious immigrants and vaccination as possible preventive measures. The next-generation matrix (NGM) Method method was used to calculate the effective reproduction number (R0). Using the Routh-Hurwitz Criterion, a disease-free equilibrium point (DFE) was discovered and It was demonstrated to have local asymptotic stability if (R0< 1), and unstable in every other case. Additionally, DFE was discovered to be quadratic Lyapunov stable and globally asymptotically stable. Additionally, the model parameters’ sensitivity analysis on the (R0) was carried out using the central manifold theory for the bifurcation analysis, and the analysis’s normalized forward sensitivity index method. MATLAB software was utilized to do numerical analysis for simulation analysis. The findings of the simulated data showed that a higher vaccination rate and fewer infectious immigrants would slow the development of the decline, as shown visually.

2024-08-15

## How to Cite

1.
Younas H, Ahmad I, Ali N, Haq IU, Daher Albalwi M, Muhammad S, Shuaib M. Modeling Rabies Dynamics: The Impact of Vaccination and Infectious Immigrants on Public Health. Contemp. Math. [Internet]. 2024 Aug. 15 [cited 2024 Sep. 12];5(3):3255-79. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/5010

Research Article