SIS and SIR Epidemic Models Under Virtual Dispersal

Autor: Carlos Castillo-Chavez, Charles Perrings, Yun Kang, Derdei Bichara, Richard D. Horan
Rok vydání: 2015
Předmět:
Strongly connected component
Computer science
General Mathematics
Immunology
Basic Reproduction Number
Dynamical Systems (math.DS)
Communicable Diseases
Models
Biological
01 natural sciences
Measure (mathematics)
Article
General Biochemistry
Genetics and Molecular Biology
03 medical and health sciences
Matrix (mathematics)
Risk Factors
FOS: Mathematics
Disease Transmission
Infectious
Humans
Applied mathematics
Mathematics - Dynamical Systems
0101 mathematics
Quantitative Biology - Populations and Evolution
Epidemics
Simulation
030304 developmental biology
General Environmental Science
Pharmacology
0303 health sciences
Models
Statistical
General Neuroscience
Populations and Evolution (q-bio.PE)
Mathematical Concepts
Function (mathematics)
010101 applied mathematics
Computational Theory and Mathematics
FOS: Biological sciences
Biological dispersal
34D23
92D25
60K35
General Agricultural and Biological Sciences
Constant (mathematics)
Epidemic model
Basic reproduction number
Zdroj: Bulletin of Mathematical Biology. 77:2004-2034
ISSN: 1522-9602
0092-8240
DOI: 10.1007/s11538-015-0113-5
Popis: We develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure contact rates that are used in the traditional multi-group epidemic models with heterogeneous mixing. We apply this approach to a general n-patch SIS model whose basic reproduction number [Formula: see text] is computed as a function of a patch residence-time matrix [Formula: see text]. Our analysis implies that the resulting n-patch SIS model has robust dynamics when patches are strongly connected: There is a unique globally stable endemic equilibrium when [Formula: see text], while the disease-free equilibrium is globally stable when [Formula: see text]. Our further analysis indicates that the dispersal behavior described by the residence-time matrix [Formula: see text] has profound effects on the disease dynamics at the single patch level with consequences that proper dispersal behavior along with the local environmental risk can either promote or eliminate the endemic in particular patches. Our work highlights the impact of residence-time matrix if the patches are not strongly connected. Our framework can be generalized in other endemic and disease outbreak models. As an illustration, we apply our framework to a two-patch SIR single-outbreak epidemic model where the process of disease invasion is connected to the final epidemic size relationship. We also explore the impact of disease-prevalence-driven decision using a phenomenological modeling approach in order to contrast the role of constant versus state-dependent [Formula: see text] on disease dynamics.
Databáze: OpenAIRE
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