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
The night falls late in Xizang Autonomous Region.In summer,the sun still scorches even at seven or eight in the evening.Ma Dan,a performing arts teacher with Shannan No.1 Middle School,was training 40 Tibetan students...The night falls late in Xizang Autonomous Region.In summer,the sun still scorches even at seven or eight in the evening.Ma Dan,a performing arts teacher with Shannan No.1 Middle School,was training 40 Tibetan students of the Kelsang Metok Cheerleading team.They sweated profusely as they danced on the playground.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.
文摘The night falls late in Xizang Autonomous Region.In summer,the sun still scorches even at seven or eight in the evening.Ma Dan,a performing arts teacher with Shannan No.1 Middle School,was training 40 Tibetan students of the Kelsang Metok Cheerleading team.They sweated profusely as they danced on the playground.
