5,390 research outputs found
On the dynamics of a class of multi-group models for vector-borne diseases
The resurgence of vector-borne diseases is an increasing public health
concern, and there is a need for a better understanding of their dynamics. For
a number of diseases, e.g. dengue and chikungunya, this resurgence occurs
mostly in urban environments, which are naturally very heterogeneous,
particularly due to population circulation. In this scenario, there is an
increasing interest in both multi-patch and multi-group models for such
diseases. In this work, we study the dynamics of a vector borne disease within
a class of multi-group models that extends the classical Bailey-Dietz model.
This class includes many of the proposed models in the literature, and it can
accommodate various functional forms of the infection force. For such models,
the vector-host/host-vector contact network topology gives rise to a bipartite
graph which has different properties from the ones usually found in directly
transmitted diseases. Under the assumption that the contact network is strongly
connected, we can define the basic reproductive number and show
that this system has only two equilibria: the so called disease free
equilibrium (DFE); and a unique interior equilibrium---usually termed the
endemic equilibrium (EE)---that exists if, and only if, . We
also show that, if , then the DFE equilibrium is globally
asymptotically stable, while when , we have that the EE is
globally asymptotically stable
Parasite spill-back from domestic hosts may induce an Allee effect in wildlife hosts
The exchange of native pathogens between wild and domesticated animals can lead to novel disease dynamics. A simple model reveals that the spill-back of native parasites\ud
from domestic to wild hosts may cause a demographic Allee effect. Because parasite spill-over and spill-back decouples the abundance of parasite infectious stages from the abundance of the wild host population, parasitism and mortality of the wild host population increases non-linearly as host abundance decreases. Analogous to the effects of satiation of generalist predators, parasite spill-back can produce an unstable equilibrium in the abundance of the host population above which the host population persists and below which it is at risk of extirpation. These effects are likely to be most pronounced in systems where the parasite has a high efficiency of transmission from domestic to wild host populations due to prolonged sympatry, disease vectors, or proximity of domesticated populations to wildlife migratory corridors
Compositional Model Repositories via Dynamic Constraint Satisfaction with Order-of-Magnitude Preferences
The predominant knowledge-based approach to automated model construction,
compositional modelling, employs a set of models of particular functional
components. Its inference mechanism takes a scenario describing the constituent
interacting components of a system and translates it into a useful mathematical
model. This paper presents a novel compositional modelling approach aimed at
building model repositories. It furthers the field in two respects. Firstly, it
expands the application domain of compositional modelling to systems that can
not be easily described in terms of interacting functional components, such as
ecological systems. Secondly, it enables the incorporation of user preferences
into the model selection process. These features are achieved by casting the
compositional modelling problem as an activity-based dynamic preference
constraint satisfaction problem, where the dynamic constraints describe the
restrictions imposed over the composition of partial models and the preferences
correspond to those of the user of the automated modeller. In addition, the
preference levels are represented through the use of symbolic values that
differ in orders of magnitude
Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics
One of the mechanisms that ensure cancer robustness is tumor heterogeneity,
and its effects on tumor cells dynamics have to be taken into account when
studying cancer progression. There is no unifying theoretical framework in
mathematical modeling of carcinogenesis that would account for parametric
heterogeneity. Here we formulate a modeling approach that naturally takes stock
of inherent cancer cell heterogeneity and illustrate it with a model of
interaction between a tumor and an oncolytic virus. We show that several
phenomena that are absent in homogeneous models, such as cancer recurrence,
tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate
that, within the applied modeling framework, to overcome the adverse effect of
tumor cell heterogeneity on cancer progression, a heterogeneous population of
an oncolytic virus must be used. Heterogeneity in parameters of the model, such
as tumor cell susceptibility to virus infection and virus replication rate, can
lead to complex, time-dependent behaviors of the tumor. Thus, irregular,
quasi-chaotic behavior of the tumor-virus system can be caused not only by
random perturbations but also by the heterogeneity of the tumor and the virus.
The modeling approach described here reveals the importance of tumor cell and
virus heterogeneity for the outcome of cancer therapy. It should be
straightforward to apply these techniques to mathematical modeling of other
types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc
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