  We formulate a compartmental model for the propagation of a respiratory
disease in a patchy environment. The patches are connected through the mobility
of individuals, and we assume that disease transmission and recovery are
possible during travel. Moreover, the migration terms are assumed to depend on
the distance between patches and the perceived severity of the disease. The
positivity and boundedness of the model solutions are discussed. We
analytically show the existence and global asymptotic stability of the
disease-free equilibrium. We study three different network topologies
numerically and find that underlying network structure is crucial for disease
transmission. Further numerical simulations reveal that infection during travel
has the potential to change the stability of disease-free equilibrium from
stable to unstable. The coupling strength and transmission coefficients are
also very crucial in disease propagation. Different exit screening scenarios
indicate that the patch with the highest prevalence may have adverse effects
but other patches will be benefited from exit screening. Furthermore, while
studying the multi-strain dynamics, it is observed that two co-circulating
strains will not persist simultaneously in the community but only one of the
strains may persist in the long run. Transmission coefficients corresponding to
the second strain are very crucial and show threshold like behavior with
respect to the equilibrium density of the second strain.
