SIS and SIR Epidemic Models Under Virtual Dispersal.
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.
SAL Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ, 85287, USA. derdei.bichara@asu.edu.
Derdei
D
Bichara
Sciences and Mathematics Faculty, College of Letters and Sciences, Arizona State University, Mesa, AZ, 85212, USA. yun.kang@asu.edu.
Yun
Y
Kang
SAL Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ, 85287, USA. ccchavez@asu.edu.
Carlos
C
Castillo-Chavez
Department of Agricultural, Food and Resource Economics, Michigan State University, East Lansing, MI, 48824, USA. horan@msu.edu.
Richard
R
Horan
School of Life Sciences, Arizona State University, Tempe, AZ, 85287, USA. Charles.Perrings@asu.edu.
Charles
C
Perrings
D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission; D018562:Disease Transmission, Infectious / Q000706:statistics & numerical data; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D015233:Models, Statistical; D012307:Risk Factors
Adaptive behavior; Dispersal; Epidemiology; Final size relationship; Global stability; Residence times; SIS–SIR models