A NONLOCAL AND TIME-DELAYED REACTION-DIFFUSION MODEL OF DENGUE TRANSMISSION
A nonlocal and time-delayed reaction-diffusion model of dengue fever is first proposed that incorporates the aquatic stage, the winged stage, and the incubation periods of the dengue virus within mosquitos and hosts. Then the basic reproduction number R₀ is established for the model system, and an e...
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| Veröffentlicht in: | SIAM journal on applied mathematics 2011-01, Vol.71 (1), p.147-168 |
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| creator | WANG, WENDI ZHAO, XIAO-QIANG |
| description | A nonlocal and time-delayed reaction-diffusion model of dengue fever is first proposed that incorporates the aquatic stage, the winged stage, and the incubation periods of the dengue virus within mosquitos and hosts. Then the basic reproduction number R₀ is established for the model system, and an explicit formula of R₀ is obtained in the case of spatially homogeneous infections. It is shown that this R₀ gives the threshold dynamics in the sense that the disease-free equilibrium is asymptotically stable if R₀ < 1 and the disease is uniformly persistent if R₀ > 1. The influences of diffusion coefficients, time delays, and infection heterogeneity on the spread of the disease are also studied via numerical simulations. It turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections. |
| doi_str_mv | 10.1137/090775890 |
| format | Article |
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It turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections.</description><identifier>ISSN: 0036-1399</identifier><identifier>EISSN: 1095-712X</identifier><identifier>DOI: 10.1137/090775890</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Asymptotic properties ; Bites and stings ; Dengue ; Dengue fever ; Dengue virus ; Diffusion ; Diffusion coefficient ; Disease models ; Disease transmission ; Dynamical systems ; Dynamics ; Eigenvalues ; Epidemiology ; Fever ; Heterogeneity ; Infections ; Mathematical models ; Mosquitos ; Reproduction ; Studies ; Time delay</subject><ispartof>SIAM journal on applied mathematics, 2011-01, Vol.71 (1), p.147-168</ispartof><rights>Copyright ©2011 Society for Industrial and Applied Mathematics</rights><rights>Copyright Society for Industrial and Applied Mathematics 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c409t-2ad461a112df24d266860f913badb9ea4b0dca5c63a4652b2aace6c66945425d3</citedby><cites>FETCH-LOGICAL-c409t-2ad461a112df24d266860f913badb9ea4b0dca5c63a4652b2aace6c66945425d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/41111582$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/41111582$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,3183,27923,27924,58016,58020,58249,58253</link.rule.ids></links><search><creatorcontrib>WANG, WENDI</creatorcontrib><creatorcontrib>ZHAO, XIAO-QIANG</creatorcontrib><title>A NONLOCAL AND TIME-DELAYED REACTION-DIFFUSION MODEL OF DENGUE TRANSMISSION</title><title>SIAM journal on applied mathematics</title><description>A nonlocal and time-delayed reaction-diffusion model of dengue fever is first proposed that incorporates the aquatic stage, the winged stage, and the incubation periods of the dengue virus within mosquitos and hosts. Then the basic reproduction number R₀ is established for the model system, and an explicit formula of R₀ is obtained in the case of spatially homogeneous infections. It is shown that this R₀ gives the threshold dynamics in the sense that the disease-free equilibrium is asymptotically stable if R₀ < 1 and the disease is uniformly persistent if R₀ > 1. The influences of diffusion coefficients, time delays, and infection heterogeneity on the spread of the disease are also studied via numerical simulations. It turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections.</description><subject>Asymptotic properties</subject><subject>Bites and stings</subject><subject>Dengue</subject><subject>Dengue fever</subject><subject>Dengue virus</subject><subject>Diffusion</subject><subject>Diffusion coefficient</subject><subject>Disease models</subject><subject>Disease transmission</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Eigenvalues</subject><subject>Epidemiology</subject><subject>Fever</subject><subject>Heterogeneity</subject><subject>Infections</subject><subject>Mathematical models</subject><subject>Mosquitos</subject><subject>Reproduction</subject><subject>Studies</subject><subject>Time 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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; LOCUS - SIAM's Online Journal Archive |
| subjects | Asymptotic properties Bites and stings Dengue Dengue fever Dengue virus Diffusion Diffusion coefficient Disease models Disease transmission Dynamical systems Dynamics Eigenvalues Epidemiology Fever Heterogeneity Infections Mathematical models Mosquitos Reproduction Studies Time delay |
| title | A NONLOCAL AND TIME-DELAYED REACTION-DIFFUSION MODEL OF DENGUE TRANSMISSION |
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