种群与进化
The human gut microbiota is a complex ecosystem that affects a range of human physiology. In order to explore the dynamics of the human gut microbiota, we used a system of ordinary differential equations to model mathematically the biomass…
This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using standard pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial…
Understanding the timing of the peak of a disease outbreak forms an important part of epidemic forecasting. In many cases, such information is essential for planning increased hospital bed demand and for designing of public health…
Many infectious diseases are comprised of multiple strains with examples including Influenza, tuberculosis, and Dengue virus. The time evolution of such systems is linked to a complex landscape shaped by interactions between competing…
In this paper, we consider the infection-age-dependent Kermack--McKendrick model in which host individuals are distributed in a continuous state space. To provide a mathematical foundation for the heterogeneous model, we develop a…
The U.S. Covid-19 data exhibit a high-frequency oscillation along a low-frequency wave for outbreaks. There is no model to account for it. A modified SIR model is proposed to explain this spiking phenomenon. It is also used to best-fit the…
The Lotka-Volterra model of competition has been studied by numerical simulations using the Runge-Kutta-Fehlberg algorithm. The stable fixed points, unstable fixed point, saddle node, basins of attraction, and the separatices are found. The…
We present a minimal model to describe the onset of collective motion seen when a population of locusts are placed in an annular arena. At low densities motion is disordered, while at high densities locusts march in a common direction,…
Relating forest productivity to local variations in forest structure has been a long-standing challenge. Previous studies often focused on the connection between forest structure and stand-level photosynthesis (GPP). However, biomass…
We build and study an individual based model of the telomere length's evolution in a population across multiple generations. This model is a continuous time typed branching process, where the type of an individual includes its gamete mean…
In evolutionary biology, phylogenetic trees are commonly inferred from a set of characters (partitions) of a collection of biological entities (e.g., species or individuals in a population). Such characters naturally arise from molecular…
Understanding the mutational history of tumor cells is a critical endeavor in unraveling the mechanisms underlying cancer. Since the modeling of tumor cell evolution employs labeled trees, researchers are motivated to develop different…
In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on…
The illness-death model for chronic conditions is combined with a renewal equation for the number of newborns taking into account possibly different fertility rates in the healthy and diseased parts of the population. The resulting boundary…
Temporal environmental noise (EN) is a prevalent natural phenomenon that controls population and community dynamics, shaping the destiny of biological species and genetic types. Conventional theoretical models often depict EN as a Markovian…
What is the long term dynamics of the Covid-19 pandemic? How will it end? Here we constructed an infectious disease model with testing and analyzed the existence and stability of its endemic states. For a large parameter set, including…
There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can…
In harsh environments, organisms may self-organize into spatially patterned systems in various ways. So far, studies of ecosystem spatial self-organization have primarily focused on apparent orders reflected by regular patterns. However,…
Developmental bias plays a major role in phenotypic evolution. Some researchers have argued that phenotypes, regulated by development, can only evolve along restricted trajectory under certain scenarios, such as the case for mammalian molar…
Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…