Third International Conference on Applications of Mathematics to Nonlinear Sciences.
Electron. J. Diff. Eqns., conf. 27 (2024), pp. 75-95.

Title: Impact  of vaccination and sterilization on the transmission dynamics of rabies

Authors: Vijai Shanker Verma (Deen Dayal Upadhyaya Gorakhpur Univ., India)
              Laxman Bahadur Kunwar (Tribhuvan Univ., Birgunj, Nepal)
 
Abstract: 
We have constructed a mathematical model by dividing the dog and human 
populations into eight compartments as the rabies virus is likely to 
spread in both populations. In the model, disease-controlling strategies 
such as vaccination, sterilization and culling are taken into 
consideration, and their impact is studied. 
The current study assumes that dogs can transmit rabies among dogs 
as well as to human population. We have applied the next-generation matrix
 technique to compute the basic reproduction number. Also, each 
parameters involved are subjected to sensitivity analysis using the 
approach of normalized sensitivity index. 
The disease-free (or rabies-free) and endemic-equilibrium points are 
discovered analytically. The endemic equilibrium point is shown to be
locally asymptotically stable.
The numerical simulations, which use approximations 
for parameter values, shows that effective method for controlling rabies 
transmission is a combination of vaccination, sterilization and culling 
of infected dogs. The findings indicate that the annual dog birth rate 
is also a critical factor in affecting the rabies virus spread.

Published August 20, 2024.
Math Subject Classifications: 92B05.
Key Words: Equilibrium point; basic reproduction number; stability; next-generation matrix; vaccination;  existence of solutions.