Numerical equilibrium analysis for structured consumer resource models

In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for “Daphnia consuming algae” models in C-code. The results obtained by way of this implementation are shown in the form of graphs

Numerical Bifurcation Analysis of Physiologically Structured Populations: Consumer-Resource, Cannibalistic and Trophic Models

With the aim of applying numerical methods, we develop a formalism for physiologically structured population models in a new generality that includes con- sumer resource, cannibalism and trophic models. The dynamics at the population level are formulated as a system of Volterra functional equations coupled to ODE. For this general class we develop numerical methods to continue equilibria with respect to a parameter, detect transcritical and saddle-node bifurcations and compute curves in parameter planes along which these bifurcations occur. The methods combine curve continuation, ODE solvers and test functions. Finally we apply the method to the above models using existing data for Daphnia magna consuming Algae, and for Perca fluviatilis feeding on Daphnia magna. In particular we validate the methods by deriving expressions for equilibria and bifurcations with respect to which we compute rrors, and by comparing the obtained curves with curves that were computed earlier with other methods. We also present new curves to show how the methods can easily be applied to derive new biological insight. Schemes of algorithms are included

Stability analysis of a renewal equation for cell population dynamics with quiescence

We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two subpopulations, and regulation of the recruitment of quiescent cells. We formulate the model as a pair of renewal equations and apply a rather recent general result to prove that (in)stability of equilibria can be analyzed by locating roots of characteristic equations. We are led to a parameter plane analysis of a characteristic equation, which has not been analyzed in this way so far. We conclude with how quiescence of cells as well as two submodels for cell division may influence the possibility of destabilization via oscillations

Stability analysis of multi-compartment models for cell production systems

We study two-and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the two-compartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result

A model for stem cell population dynamics with regulated maturation delay

We develop a structured population model for the maturation process of stem cells in the form of a state-dependent delay differential equation. Moreover, results on existence, uniqueness and positivity of solutions as well as conditions of existence for equilibria and representations of these are established. We give biological interpretations for the conditions of existence of equilibria

Global dynamics of two-compartment models for cell production systems with regulatory mechanisms

We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell division rate or the self-renewal fraction regulated by the number of mature cells. The two-compartment systems constitute a basic version of the multicompartment models proposed recently by Marciniak-Czochra and collaborators [25] to investigate the dynamics of the hematopoietic system. Using global stability analysis, we compare different regulatory mechanisms. For both models, we show that there exists a unique positive equilibrium that is globally asymptotically stable if and only if the respective reproduction numbers exceed one. The proof is based on constructing Lyapunov functions, which are appropriate to handle the specific nonlinearities of the model. Additionally, we propose a new model to test biological hypothesis on the regulation of the fraction of differentiating cells. We show that such regulatory mechanism is incapable of maintaining homeostasis and leads to unbounded cell growth. Potential biological implications are discussed

Reconceptualising Personas Across Cultures: Archetypes, Stereotypes & Collective Personas in Pastoral Namibia

The paucity of projects where persona is the research foci and a lack of consensus on this artefact keep many reticent about its purpose and value. Besides crafting personas is expected to differ across cultures, which contrasts the advancements in Western theory with studies and progress in other sites. We postulate User-Created Personas reveal specific characteristics of situated contexts by allowing laypeople to design persona artefacts in their own terms. Hence analysing four persona sessions with an ethnic group in pastoral Namibia –ovaHerero– brought up a set of fundamental questions around the persona artefact regarding stereotypes, archetypes, and collective persona representations: (1) to what extent user depictions are stereotypical or archetypal? If stereotypes prime (2) to what degree are current personas a useful method to represent end-users in technology design? And, (3) how can we ultimately read accounts not conforming to mainstream individual persona descriptions but to collectives

Modeling Within-Host Dynamics of Influenza Virus Infection Including Immune Responses

Influenza virus infection remains a public health problem worldwide. The mechanisms underlying viral control during an uncomplicated influenza virus infection are not fully understood. Here, we developed a mathematical model including both innate and adaptive immune responses to study the within-host dynamics of equine influenza virus infection in horses. By comparing modeling predictions with both interferon and viral kinetic data, we examined the relative roles of target cell availability, and innate and adaptive immune responses in controlling the virus. Our results show that the rapid and substantial viral decline (about 2 to 4 logs within 1 day) after the peak can be explained by the killing of infected cells mediated by interferon activated cells, such as natural killer cells, during the innate immune response. After the viral load declines to a lower level, the loss of interferon-induced antiviral effect and an increased availability of target cells due to loss of the antiviral state can explain the observed short phase of viral plateau in which the viral level remains unchanged or even experiences a minor second peak in some animals. An adaptive immune response is needed in our model to explain the eventual viral clearance. This study provides a quantitative understanding of the biological factors that can explain the viral and interferon kinetics during a typical influenza virus infection