Studying spread of epidemics and diseases are world wide problems
especially during the current time where the whole world is suffering
from COVID-19 pandemic. Antimicrobial resistance (AMR) and waning
vaccination are classified as world wide problems. Both depend on the
exposure time to antibiotic and vaccination. Here, a simple model for
competition between drug resistant and drug sensitive bacteria is given.
Conditions for local stability are investigated which agree with
observation. Existence of positive solution in the AMR complex networks
is proved. Dynamics of the identical AMR models are explored with
different topologies of complex networks such as global, star, line and
unidirectional line networks coupled through their susceptible states.
Chaotic attractors are shown to be existed as the AMR models are located
on all the indicted topologies of complex networks. Thus, it is found
that the dynamics of the AMR model become more complicated as it is
located on either integer-order or fractional-order complex networks.
Furthermore, a discretized version of the fractional AMR model is
presented. Complex dynamics such as existence of Neimark–Sacker, flip
bifurcations, coexistence of multi attractors, homoclinic connections
and multi closed invariant curves are investigated. Basin sets of
attraction are also computed. Finally, the discretized system is located
on complex networks with different topologies which also show rich
variety of complex dynamics. Also, 0-1 test is used to verify the
existence of unpredictable dynamics. So, studying the dynamics of AMR
models on complex networks is very helpful to understand the mechanism
of spread of diseases.