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We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high friction limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic aggregation...
Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling...
In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity....
We propose and analyze a nonlinear mathematical model of hematopoiesis,
describing the dynamics of stem cell population subject to impulsive
perturbations. This is a system of two age-structured partial differential
equations with impulses. By integrating these equations over the
age, we obtain a system of two nonlinear impulsive differential equations with
several discrete delays. This system describes the evolution of the total
hematopoietic stem cell populations with impulses. We first examine...
The blow-up of solutions for a parabolic equation with nonlocal exponential nonlinearity is studied.
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