DCDS-B
In this paper, we consider global stability for a heroin model with
two distributed delays. The basic reproduction number of the heroin
spread is obtained, which completely determines the stability of the
equilibria. Using the direct Lyapunov method with Volterra type
Lyapunov function, we show that the drug use-free equilibrium is
globally asymptotically stable if the basic reproduction number is
less than one, and the unique drug spread equilibrium is globally
asymptotically stable if the basic reproduction number is greater
than one.
MBE
In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproductive number $\mathcal R_0$ is derived. By using the method of Lyapunov function, the global dynamics of the PDE model is further established, and the results show that the basic reproduction number $\mathcal R_0$ determines the transmission dynamics of vector-borne diseases: the disease-free equilibrium is globally asymptotically stable if $\mathcal R_0≤ 1$, and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$. The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one.
MBE
A classical epidemiological framework is used to provide a preliminary cost analysis of the effects of quarantine and isolation on the dynamics of infectious diseases for which no treatment or immediate diagnosis tools are available.
Within this framework we consider the cost incurred from the implementation of three types of dynamic control strategies. Taking the context of the 2003 SARS outbreak in Hong Kong as an example, we use a simple cost function to compare the total cost of each mixed (quarantine and isolation) control strategy from a public health resource allocation perspective.
The goal is to extend existing epi-economics methodology by developing a theoretical framework of dynamic quarantine strategies aimed at emerging diseases, by drawing upon the large body of literature on the dynamics of infectious diseases.
We find that the total cost decreases with increases in the quarantine rates past a critical value, regardless of the resource allocation strategy.
In the case of a manageable outbreak resources must be used early to achieve the best results whereas in case of an unmanageable outbreak, a constant-effort strategy seems the best among our limited plausible sets.
MBE
This article
focuses on the study of an age-structured
two-strain model with super-infection. The explicit expression of
basic reproduction numbers and the invasion reproduction numbers
corresponding to strain one and strain two are obtained. It is
shown that the infection-free steady state is globally stable if
the basic reproductive number $ R_0 $ is below one. Existence
of strain one and strain two exclusive equilibria is established.
Conditions for local stability or instability
of the exclusive equilibria of the
strain one and strain two are established. Existence of
coexistence equilibrium is also obtained under the condition that both
invasion reproduction numbers are larger than one.
DCDS-B
An infection-age-structured epidemic model
with environmental bacterial infection is investigated in this
paper. It is assumed that the infective population is
structured according to age of infection, and the infectivity of the treated individuals is reduced but
varies with the infection-age.
An explicit formula for the reproductive number $ \Re_0$ of the model
is obtained. By constructing a suitable Lyapunov function, the
global stability of the infection-free equilibrium in the system
is obtained for $\Re_0<1$. It is also shown that if the
reproduction number $\Re_0>1$, then the system has a unique endemic
equilibrium which is locally asymptotically stable. Furthermore, if
the reproduction number $\Re_0>1$, the system is permanent. When
the treatment rate and the transmission rate are both independent
of infection age, the system of partial differential equations
(PDEs) reduces to a system of ordinary differential equations
(ODEs). In this special case, it is shown that the global dynamics
of the system can be determined by the basic reproductive number.
MBE
We consider a model for a disease with
two competing strains and vaccination.
The vaccine provides complete protection against one of the strains
(strain 2) but only
partial protection
against the other (strain 1). The partial protection leads to
existence of subthreshold equilibria of strain 1. If the first strain
mutates into the second, there are subthreshold coexistence equilibria
when both vaccine-dependent reproduction numbers are below one.
Thus, a vaccine that is specific toward the second strain
and that, in absence of other strains, should be able to eliminate
the second strain
by reducing its reproduction number below one,
cannot do so because it provides only
partial protection to another strain that mutates into the second strain.
keywords:
latent stage
,
coexistence
,
strongly
subthreshold coexistence
,
vaccine enhanced pathogen polymorphism.
,
multiple coexistence equilibria
,
multiple endemic equilibria
,
mutation
,
backward bifurcation
,
latent-stage progression age structure
,
alternating stability
,
vaccination
DCDS-B
This paper investigates a two strain SIS model with diffusion, spatially heterogeneous coefficients of the reaction part and distinct diffusion rates of the separate epidemiological classes. First, it is shown that the model has bounded classical solutions. Next, it is established that the model with spatially homogeneous coefficients leads to competitive exclusion and no coexistence is possible in this case. Furthermore, it is proved that if the invasion number of strain $j$ is larger than one, then the equilibrium of strain $i$ is unstable; if, on the other hand, the invasion number of strain $j$ is smaller than one, then the equilibrium of strain $i$ is neutrally stable. In the case when all diffusion rates are equal, global results on competitive exclusion and coexistence of the strains are established. Finally, evolution of dispersal scenario is considered and it is shown that the equilibrium of the strain with the larger diffusion rate is unstable. Simulations suggest that in this case the equilibrium of the strain with the smaller diffusion rate is stable.
