In this paper, we construct an SIR epidemic model with a modified Beddington–DeAngelis type incidence rate and saturated treatment rate. We modify the incidence rateto incorporate the isolation of infected individual...In this paper, we construct an SIR epidemic model with a modified Beddington–DeAngelis type incidence rate and saturated treatment rate. We modify the incidence rateto incorporate the isolation of infected individuals after detection, and separation of somesusceptible individuals from the rest to avoid the infection, without an increase in thenumber of classes. We find that the system has a unique disease-free equilibrium (DFE)which is locally asymptotically stable when the reproduction number is less than unity.The multiple endemic equilibria may exist irrespective of the basic reproduction number.The existence of bistability is encountered. Supercritical transcritical (forward), as wellas subcritical transcritical (backward) bifurcation, may occur at R0 = 1 where contactrate, β = β∗ acts as the bifurcation parameter. Therefore, DFE need not be globallystable. The conditions for the existence of Andronov–Hopf bifurcation are deduced withmaximum treatment capacity, c = c0 as the bifurcation parameter. The impacts of isolation of confirmed infected cases and separation of some susceptible from rest are studiednumerically as well as the effect of saturation in treatment. The existence of chaoticbehavior is deduced by showing the maximum Lyapunov exponent to be positive as wellas the sensitivity to initial conditions. The computation of the Kalpan–Yorke dimensionto be fractional confirms the existence of fractal-type strange attractor. The positiveKolmogorov–Sinai entropy further strengthens the claim of the existence of chaos.展开更多
Objective： To investigate the effect of Ermiao Recipe （二妙方, EMR） with medicinal guide Angelicae Pubescentis Radix （APR） on the homing of bone marrow stem cells （BMSCs） to focal zone in osteoarthritis （OA） ...Objective： To investigate the effect of Ermiao Recipe （二妙方, EMR） with medicinal guide Angelicae Pubescentis Radix （APR） on the homing of bone marrow stem cells （BMSCs） to focal zone in osteoarthritis （OA） rats. Methods： Forty-eight Sprague-Dawley rats were randomly assigned to the sham-operated, model, EMR, and EMR plus APR groups （12 rats in each group）. The OA rat model was induced by anterior cruciate ligament transection and medial meniscus resection. All rats were injected with recombinant human granulocyta colony- stimulating factor [rhG-CSF, 30 μg/（kg.d） for continuous 7 days], and rats in the EMR and EMR plus APR groups were treated with EMR or EMR plus APR at 1.6 or 1.9 g/（kg.d） for 3 or 6 weeks, respectively. Cartilage histopathologic changes were observed by hematoxylin and eosin staining. Chondrocytes apoptosis and cartilage matrix components were tested by transferase-mediated deoxyuridine triphosphate-biotin nick end labeling assay and special staining. Interleukin-1β （IL-1 β）, tumor necrosis factor α （TNF-α）, bone morphogenetic protein 2 （BMP-2）, and transforming growth factor beta-1 （TGF-β1） in serum were detected by enzyme-linked immunosorbent assay or radioimmunoassay assay. Matrix metalloproteinase （MMP）-13, tissue inhibitors of metalloproteinase （TIMP）-1, bromodeoxyuridine （BrdU）, cluster of differentiation 34 （CD34）, and stromal cell derived factor 1 （SDF-1） were measured by immunohistochemistry assay. Results： EMR and EMR plus APR significantly inhibited articular cartilage damage and synovium inflammation in OA rats at 3 or 6 weeks of treatment, the most obvious changes in these parameters were found in the EMR plus APR group. At 6 weeks, compared with EMR treatment, EMR plus APR remarkably inhibited chondrocytes apoptosis and the release of IL-1β and TNF- a, obviously decreased MMP-13 expression, and significantly increased expressions of proteoglycan, collagen, type 11 collagen and TIMP-1, serum levels of BMP-2 and TGF- 131 as well as expressions of BrdU, CD34 and SDF-1 in cartilage articular （P〈0.01 or P〈0.05 ）. Conclusion： The medicinal guide APR improved the therapeutic effects of EMR on OA rats by promoting directional homing of BMSCs to focal zone.展开更多
文摘In this paper, we construct an SIR epidemic model with a modified Beddington–DeAngelis type incidence rate and saturated treatment rate. We modify the incidence rateto incorporate the isolation of infected individuals after detection, and separation of somesusceptible individuals from the rest to avoid the infection, without an increase in thenumber of classes. We find that the system has a unique disease-free equilibrium (DFE)which is locally asymptotically stable when the reproduction number is less than unity.The multiple endemic equilibria may exist irrespective of the basic reproduction number.The existence of bistability is encountered. Supercritical transcritical (forward), as wellas subcritical transcritical (backward) bifurcation, may occur at R0 = 1 where contactrate, β = β∗ acts as the bifurcation parameter. Therefore, DFE need not be globallystable. The conditions for the existence of Andronov–Hopf bifurcation are deduced withmaximum treatment capacity, c = c0 as the bifurcation parameter. The impacts of isolation of confirmed infected cases and separation of some susceptible from rest are studiednumerically as well as the effect of saturation in treatment. The existence of chaoticbehavior is deduced by showing the maximum Lyapunov exponent to be positive as wellas the sensitivity to initial conditions. The computation of the Kalpan–Yorke dimensionto be fractional confirms the existence of fractal-type strange attractor. The positiveKolmogorov–Sinai entropy further strengthens the claim of the existence of chaos.
基金Supported by National Natural Science Foundation of China(No.81072900)
文摘Objective： To investigate the effect of Ermiao Recipe （二妙方, EMR） with medicinal guide Angelicae Pubescentis Radix （APR） on the homing of bone marrow stem cells （BMSCs） to focal zone in osteoarthritis （OA） rats. Methods： Forty-eight Sprague-Dawley rats were randomly assigned to the sham-operated, model, EMR, and EMR plus APR groups （12 rats in each group）. The OA rat model was induced by anterior cruciate ligament transection and medial meniscus resection. All rats were injected with recombinant human granulocyta colony- stimulating factor [rhG-CSF, 30 μg/（kg.d） for continuous 7 days], and rats in the EMR and EMR plus APR groups were treated with EMR or EMR plus APR at 1.6 or 1.9 g/（kg.d） for 3 or 6 weeks, respectively. Cartilage histopathologic changes were observed by hematoxylin and eosin staining. Chondrocytes apoptosis and cartilage matrix components were tested by transferase-mediated deoxyuridine triphosphate-biotin nick end labeling assay and special staining. Interleukin-1β （IL-1 β）, tumor necrosis factor α （TNF-α）, bone morphogenetic protein 2 （BMP-2）, and transforming growth factor beta-1 （TGF-β1） in serum were detected by enzyme-linked immunosorbent assay or radioimmunoassay assay. Matrix metalloproteinase （MMP）-13, tissue inhibitors of metalloproteinase （TIMP）-1, bromodeoxyuridine （BrdU）, cluster of differentiation 34 （CD34）, and stromal cell derived factor 1 （SDF-1） were measured by immunohistochemistry assay. Results： EMR and EMR plus APR significantly inhibited articular cartilage damage and synovium inflammation in OA rats at 3 or 6 weeks of treatment, the most obvious changes in these parameters were found in the EMR plus APR group. At 6 weeks, compared with EMR treatment, EMR plus APR remarkably inhibited chondrocytes apoptosis and the release of IL-1β and TNF- a, obviously decreased MMP-13 expression, and significantly increased expressions of proteoglycan, collagen, type 11 collagen and TIMP-1, serum levels of BMP-2 and TGF- 131 as well as expressions of BrdU, CD34 and SDF-1 in cartilage articular （P〈0.01 or P〈0.05 ）. Conclusion： The medicinal guide APR improved the therapeutic effects of EMR on OA rats by promoting directional homing of BMSCs to focal zone.
