Abstract
Rabies is a deadly viral disease transmitted through the bites of infected animals,
particularly dogs, and poses a significant threat to both animal and human populations.
This study aims to develop a multi-scale model to investigate the dynamics
of rabies transmission between stray dogs and humans. Mathematical models have
shown that vaccination can effectively eliminate rabies in vaccinated populations,
and many low-economic countries continue to suffer from rabies disease due to
the high cost of vaccines and the presence of stray dogs. We use multi-scale
modeling, a key technique in mathematical biology, to predict rabies dynamics
at different scales. Our study introduces two within-host mathematical models:
one for humans and one for stray dogs. Using a nested multi-scale approach,
we linked between-host dynamics to within-host interactions through the community
viral load concept. The mathematical analysis reveals two equilibrium points
in the between-host model: a disease-free equilibrium and an endemic equilibrium.
The within-host human model shows one disease-free equilibrium and two
endemic equilibrium points, while the stray dog model features one disease-free
equilibrium and three endemic equilibrium points. The overall multi-scale model
maintains a disease-free equilibrium and an endemic equilibrium, reflecting the
complex dynamics at the population level. All equilibrium points were shown to
be globally asymptotically stable using Lyapunov functions. Notably, the basic
reproduction number for the linked model is derived from the dynamics of stray
dogs, highlighting the influence of within-host parameters on between-host dynamics.
The results of this study demonstrate that host-specific parameters, such
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as infection rate and the average number produced by each actively infected cell,
significantly influence the population dynamics of rabies disease. These factors
affect how the infection spreads and progresses, showing that the characteristics
of the host play an important role in shaping the patterns of an epidemic.