  Mathematical modelling of epidemiological and coevolutionary dynamics is
widely being used to improve disease management strategies of infectious
diseases. Many diseases present some form of intra-host quiescent stage, also
known as covert infection, while others exhibit dormant stages in the
environment. As quiescent/dormant stages can be resistant to drug, antibiotics,
fungicide treatments, it is of practical relevance to study the influence of
these two life-history traits on the coevolutionary dynamics. We develop first
a deterministic coevolutionary model with two parasite types infecting one host
type and study analytically the stability of the dynamical system. We
specifically derive a stability condition for a five-by-five system of
equations with quiescence. Second, we develop a stochastic version of the model
to study the influence of quiescence on stochasticity of the system dynamics.
We compute the steady state distribution of the parasite types which follows a
multivariate normal distribution. Furthermore, we obtain numerical solutions
for the covariance matrix of the system under symmetric and asymmetric
quiescence rates between parasite types. When parasite strains are identical,
quiescence increases the variance of the number of infected individuals at high
transmission rate and vice versa when the transmission rate is low. However,
when there is competition between parasite strains with different quiescent
rates, quiescence generates a moving average behaviour which dampen off
stochasticity and decreases the variance of the number of infected hosts. The
strain with the highest rate of entering quiescence determines the strength of
the moving average and the magnitude of reduction of stochasticity. Thus, it is
worth investigating simple models of multi-strain parasite under
quiescence/dormancy to improve disease management strategies.
