Third International Conference on Applications of Mathematics to Nonlinear Sciences.
Electron. J. Diff. Eqns., Conference 27 (2024), pp. 7595.
Impact of vaccination and sterilization on the transmission dynamics of rabies
Vijai Shanker Verma, Laxman Bahadur Kunwar
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, diseasecontrolling 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 nextgeneration 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 diseasefree (or rabiesfree) and endemicequilibrium 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; nextgeneration matrix; vaccination; existence of solutions.
DOI: 10.58997/ejde.conf.27.v1
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Vijai Shanker Verma
Department of Mathematics and Statistics
Deen Dayal Upadhyaya Gorakhpur University, India
email: vsverma.mathstat@ddugu.ac.in


Laxman Bahadur Kunwar
Department of Mathematics
Thakur Ram Multiple Campus
Tribhuvan University, Birgunj, Nepal
email: laxman.kunwar@trmc.tu.edu.np

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