Biomaterial Database

Steady-state analysis of a continuum model for super-infection. 2009

Bard Ermentrout, and Stuart Hastings

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. bard@pitt.edu

A large system of N strains of parasite and a single host is analyzed as a function of the degree of virulence in the strains when there is super-infection between hosts (more virulent strains can infect hosts that are already infected) and within-host transition between strains that is neutral. When this small amount of local switching is allowed, steady-state solutions converge to a continuous distribution as the number of strains increases. The resulting nonlinear-nonautonomous integro-differential equation is reduced to a fourth order boundary value problem (BVP) and the existence of positive solutions is proven. The methods here and associated BVP allow for a thorough exploration of parameter space for this class of models.

UI	MeSH Term	Description	Entries
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D005075	Biological Evolution	The process of cumulative change over successive generations through which organisms acquire their distinguishing morphological and physiological characteristics.	Evolution, Biological
D006790	Host-Parasite Interactions	The relationship between an invertebrate and another organism (the host), one of which lives at the expense of the other. Traditionally excluded from definition of parasites are pathogenic BACTERIA; FUNGI; VIRUSES; and PLANTS; though they may live parasitically.	Host-Parasite Relations,Parasite-Host Relations,Host-Parasite Relationship,Parasite-Host Interactions,Host Parasite Interactions,Host Parasite Relations,Host Parasite Relationship,Host-Parasite Interaction,Host-Parasite Relation,Host-Parasite Relationships,Interaction, Host-Parasite,Interaction, Parasite-Host,Interactions, Host-Parasite,Interactions, Parasite-Host,Parasite Host Interactions,Parasite Host Relations,Parasite-Host Interaction,Parasite-Host Relation,Relation, Host-Parasite,Relation, Parasite-Host,Relations, Host-Parasite,Relations, Parasite-Host,Relationship, Host-Parasite,Relationships, Host-Parasite
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D014774	Virulence	The degree of pathogenicity within a group or species of microorganisms or viruses as indicated by case fatality rates and/or the ability of the organism to invade the tissues of the host. The pathogenic capacity of an organism is determined by its VIRULENCE FACTORS.	Pathogenicity
D015163	Superinfection	A frequent complication of drug therapy for microbial infection. It may result from opportunistic colonization following immunosuppression by the primary pathogen and can be influenced by the time interval between infections, microbial physiology, or host resistance. Experimental challenge and in vitro models are sometimes used in virulence and infectivity studies.	Microbial Superinvasion,Superinvasion, Microbial,Microbial Superinvasions,Superinfections,Superinvasions, Microbial
D017711	Nonlinear Dynamics	The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.	Chaos Theory,Models, Nonlinear,Non-linear Dynamics,Non-linear Models,Chaos Theories,Dynamics, Non-linear,Dynamics, Nonlinear,Model, Non-linear,Model, Nonlinear,Models, Non-linear,Non linear Dynamics,Non linear Models,Non-linear Dynamic,Non-linear Model,Nonlinear Dynamic,Nonlinear Model,Nonlinear Models,Theories, Chaos,Theory, Chaos
D049490	Systems Biology	Comprehensive, methodical analysis of complex biological systems by monitoring responses to perturbations of biological processes. Large scale, computerized collection and analysis of the data are used to develop and test models of biological systems.	Biology, Systems
D054884	Host-Pathogen Interactions	The interactions between a host and a pathogen, usually resulting in disease.	Host Pathogen Interaction,Host-Pathogen Relations,Pathogen-Host Interaction,Pathogen-Host Interactions,Host Pathogen Interactions,Host Pathogen Relations,Host-Pathogen Interaction,Host-Pathogen Relation,Interaction, Host Pathogen,Interaction, Host-Pathogen,Interaction, Pathogen-Host,Interactions, Host Pathogen,Interactions, Host-Pathogen,Interactions, Pathogen-Host,Pathogen Host Interaction,Pathogen Host Interactions,Pathogen Interaction, Host,Pathogen Interactions, Host,Relation, Host-Pathogen,Relations, Host-Pathogen