Mathematical modeling and analysis of harmful algal blooms in flowing habitats.

In this paper, we survey recent developments of mathematical modeling and analysis of the dynamics of harmful algae in riverine reservoirs. To make the models more realistic, a hydraulic storage zone is incorporated into a flow reactor model and new mathematical challenges arise from the loss of compactness of the solution maps. The key point in the study of the evolution dynamics is to prove the existence of global attractors for the model systems and the principal eigenvalues for the associated linearized systems without compactness.

Extinction and uniform persistence in a microbial food web with mycoloop: limiting behavior of a population model with parasitic fungi.

It is recently known that parasites provide a better picture of an ecosystem, gaining attention in theoretical ecology. Parasitic fungi belong to a food chain between zooplankton and inedible phytoplankton, called mycoloop. We consider a chemostat model that incorporates a single mycoloop, and analyze the limiting behavior of solutions, adding to previous work on steady-state analysis.

Single species growth consuming inorganic carbon with internal storage in a poorly mixed habitat.

This paper presents a PDE system modeling the growth of a single species population consuming inorganic carbon that is stored internally in a poorly mixed habitat. Inorganic carbon takes the forms of "CO2" (dissolved CO2 and carbonic acid) and "CARB" (bicarbonate and carbonate ions), which are substitutable in their effects on algal growth. We first establish a threshold type result on the extinction/persistence of the species in terms of the sign of a principal eigenvalue associated with a nonlinear eigenvalue problem.

Numerical proof for chemostat chaos of Shilnikov's type.

A classical chemostat model is considered that models the cycling of one essential abiotic element or nutrient through a food chain of three trophic levels. The long-time behavior of the model was known to exhibit complex dynamics more than 20 years ago. It is still an open problem to prove the existence of chaos analytically.

Algal competition in a water column with excessive dioxide in the atmosphere.

This paper deals with a resource competition model of two algal species in a water column with excessive dioxide in the atmosphere. First, the uniqueness of positive steady state solutions to the single-species model with two resources is established by the application of the degree theory and the strong maximum principle for the cooperative system. Second, some asymptotic behavior of the single-species model is given by comparison principle and uniform persistence theory.

Theory of a microfluidic serial dilution bioreactor for growth of planktonic and biofilm populations.

We present the theory of a microfluidic bioreactor with a two-compartment growth chamber and periodic serial dilution. In the model, coexisting planktonic and biofilm populations exchange by adsorption and detachment. The criteria for coexistence and global extinction are determined by stability analysis of the global extinction state.

Dynamics of phytoplankton communities under photoinhibition.

We analyzed a model of phytoplankton competition for light in a well-mixed water column. The model, proposed by Gerla et al. (Oikos 120:519-527, 2011), assumed inhibition of photosynthesis at high irradiance (photoinhibition).

Subfunctionalization reduces the fitness cost of gene duplication in humans by buffering dosage imbalances.

Background: Driven essentially by random genetic drift, subfunctionalization has been identified as a possible non-adaptive mechanism for the retention of duplicate genes in small-population species, where widespread deleterious mutations are likely to cause complementary loss of subfunctions across gene copies. Through subfunctionalization, duplicates become indispensable to maintain the functional requirements of the ancestral locus. Yet, gene duplication produces a dosage imbalance in the encoded proteins and thus, as investigated in this paper, subfunctionalization must be subject to the selective forces arising from the fitness bottleneck introduced by the duplication event.

Competition between microorganisms for a single limiting resource with cell quota structure and spatial variation.

Microbial populations compete for nutrient resources, and the simplest mathematical models of competition neglect differences in the nutrient content of individuals. The simplest models also assume a spatially uniform habitat. Here both of these assumptions are relaxed.

A Lotka-Volterra competition model with seasonal succession.

A complete classification for the global dynamics of a Lotka-Volterra two species competition model with seasonal succession is obtained via the stability analysis of equilibria and the theory of monotone dynamical systems. The effects of two death rates in the bad season and the proportion of the good season on the competition outcomes are also discussed.

Synchronized reproduction promotes species coexistence through reproductive facilitation.

Theories for species coexistence often emphasize niche differentiation and temporal segregation of recruitment to avoid competition. Recent work on mutualism suggested that plant species sharing pollinators provide mutual facilitation when exhibit synchronized reproduction. The facilitation on reproduction may enhance species persistence and coexistence.

Competition and coexistence in flowing habitats with a hydraulic storage zone.

This paper examines a model of a flowing water habitat with a hydraulic storage zone in which no flow occurs. In this habitat, one or two microbial populations grow while consuming a single nutrient resource. Conditions for persistence of one population and coexistence of two competing populations are derived from eigenvalue problems, the theory of bifurcation and the theory of monotone dynamical systems.

Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion.

We establish conditions which exclude periodic solutions in a simple chemostat with a single nutrient and N competing species. Growth rates are not required to be proportional to food uptake. Instead of a Lyapunov function approach, we develop and apply a multi-dimensional Bendixson-Dulac type exclusion principle based on differential forms.

The final size of a SARS epidemic model without quarantine.

In this article, we present the continuing work on a SARS model without quarantine by Hsu and Hsieh [Sze-Bi Hsu, Ying-Hen Hsieh, Modeling intervention measures and severity-dependent public response during severe acute respiratory syndrome outbreak, SIAM J. Appl. Math.

On the role of asymptomatic infection in transmission dynamics of infectious diseases.

We propose a compartmental disease transmission model with an asymptomatic (or subclinical) infective class to study the role of asymptomatic infection in the transmission dynamics of infectious diseases with asymptomatic infectives, e.g., influenza.

Impact of quarantine on the 2003 SARS outbreak: a retrospective modeling study.

During the 2003 Severe Acute Respiratory Syndrome (SARS) outbreak, traditional intervention measures such as quarantine and border control were found to be useful in containing the outbreak. We used laboratory verified SARS case data and the detailed quarantine data in Taiwan, where over 150,000 people were quarantined during the 2003 outbreak, to formulate a mathematical model which incorporates Level A quarantine (of potentially exposed contacts of suspected SARS patients) and Level B quarantine (of travelers arriving at borders from SARS affected areas) implemented in Taiwan during the outbreak. We obtain the average case fatality ratio and the daily quarantine rate for the Taiwan outbreak.

SARS outbreak, Taiwan, 2003.

We studied the severe acute respiratory syndrome (SARS) outbreak in Taiwan, using the daily case-reporting data from May 5 to June 4 to learn how it had spread so rapidly. Our results indicate that most SARS-infected persons had symptoms and were admitted before their infections were reclassified as probable cases. This finding could indicate efficient admission, slow reclassification process, or both.

A ratio-dependent food chain model and its applications to biological control.

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics.

Plasmid-bearing, plasmid-free organisms competing for two complementary nutrients in a chemostat.

A model of competition for two complementary nutrients between plasmid-bearing and plasmid-free organisms in a chemostat is proposed. A rigorous mathematical analysis of the global asymptotic behavior of the model is presented. The work extends the model of competition for a single-limited nutrient studied by Stephanopoulos and Lapidus [Chem.