15 research outputs found
Multiplicity of endemic equilibria for a diffusive SIS epidemic model with mass-action transmission mechanism
We study a diffusive SIS epidemic model with mass-action transmission
mechanism and show, under appropriate assumptions on the parameters, the
existence of multiple endemic equilibria when the basic reproduction number,
, is either less than one or greater than one. Previous studies
have left open the question of extinction of disease or persistence when
. Our results settle completely this open question. Results on
the nonexistence/existence and uniqueness of endemic equilibrium are also
presented
Existence of traveling wave solutions of a deterministic vector-host epidemic model with direct transmission
We consider an epidemic model with direct transmission given by a system of
nonlinear partial differential equations and study the existence of traveling
wave solutions. When the basic reproductive number of the considered model is
less than one, we show that there is no nontrivial traveling wave solution. On
the other hand, when the basic reproductive number is greater than one, we
prove that there is a minimum wave speed such that the system has a
traveling wave solution with speed connecting both equilibrium points for
any . Moreover, under suitable assumption on the diffusion rates, we
show that there is no traveling wave solution with speed less than . We
conclude with numerical simulations to illustrate our findings. The numerical
experiments supports the validity of our theoretical results
Competition-exclusion and coexistence in a two-strain SIS epidemic model in patchy environments
This work examines the dynamics of solutions of a two-strain SIS epidemic
model in patchy environments. The basic reproduction number is
introduced, and sufficient conditions are provided to guarantee the global
stability of the disease-free equilibrium (DFE). In particular, the DFE is
globally stable when either: (i) , where
is the total number of patches, or (ii) and the dispersal
rate of the susceptible population is large. Moreover, the questions of
competition-exclusion and coexistence of the strains are investigated when the
single-strain reproduction numbers are greater than one. In this direction,
under some appropriate hypotheses, it is shown that the strain whose basic
reproduction number and local reproduction function are the largest always
drives the other strain to extinction in the long run. Furthermore, the
asymptotic dynamics of the solutions are presented when either both strain's
local reproduction functions are spatially homogeneous or the population
dispersal rate is uniform. In the latter case, the invasion numbers are
introduced and the existence of coexistence endemic equilibrium (EE) is proved
when these invasion numbers are greater than one. Numerical simulations are
provided to complement the theoretical results.Comment: 35 page