A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 HIN1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quaranti...A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 HIN1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quarantine （isolation） strategies in reduc- ing the spread of H1N1 flu is incorporated. The model monitors the dynamics of five sub-populations （classes）, namely susceptible with high infection risk, susceptible with reduction of infection risk, infective, quarantined and recovered individuals. The model analysis includes the determination of equilibrium points and carrying out their stability analysis in terms of the threshold parameter R0. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge-Kutta method along with the sensitivity analysis of the endemic equilibrium point. The analysis and numeri- cal simulation results demonstrate that the maximum implementation of contact tracing and quarantine strategies help in reducing endemic infective class size and hence act as effective intervention strategy to control the disease. This gives a theoretical interpreta- tion to the practical experiences that the early contact tracing and quarantine strategies are criticMly important to control the outbreak of epidemics.展开更多
Influenza H1N1 has been found to exhibit oscillatory levels of incidence in large pop- ulations. Clear peaks for influenza H1N1 are observed in several countries including Vietnam each year [M. F. Boni, B. H. Manh, P....Influenza H1N1 has been found to exhibit oscillatory levels of incidence in large pop- ulations. Clear peaks for influenza H1N1 are observed in several countries including Vietnam each year [M. F. Boni, B. H. Manh, P. Q. Thai, J. Farrar, T. Hien, N. T. Hien, N. Van Kinh and P. Horby, Modelling the progression of pandemic influenza A （H1N1） in Vietnam and the opportunities for reassortment with other influenza viruses, BMC Med. 7 （2009） 43, Doi： 10.1186/1741-7015-%43]. So it is important to study seasonal forces and factors which can affect the transmission of this disease. This paper studies an SIRS epidemic model with seasonal vaccination rate. This SIRS model has a unique disease-free solution （DFS）. The value Ro, the basic reproduction number is obtained when the vaccination is a periodic function. Stability results for the DFS are obtained when R0 〈 1. The disease persists in the population and remains endemic if R0 〉 1. Also when R0 〉 1 existence of a nonzero periodic solution is proved. These results obtained for our model when the vaccination strategy is a non-constant time-dependent function.展开更多
文摘A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 HIN1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quarantine （isolation） strategies in reduc- ing the spread of H1N1 flu is incorporated. The model monitors the dynamics of five sub-populations （classes）, namely susceptible with high infection risk, susceptible with reduction of infection risk, infective, quarantined and recovered individuals. The model analysis includes the determination of equilibrium points and carrying out their stability analysis in terms of the threshold parameter R0. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge-Kutta method along with the sensitivity analysis of the endemic equilibrium point. The analysis and numeri- cal simulation results demonstrate that the maximum implementation of contact tracing and quarantine strategies help in reducing endemic infective class size and hence act as effective intervention strategy to control the disease. This gives a theoretical interpreta- tion to the practical experiences that the early contact tracing and quarantine strategies are criticMly important to control the outbreak of epidemics.
文摘Influenza H1N1 has been found to exhibit oscillatory levels of incidence in large pop- ulations. Clear peaks for influenza H1N1 are observed in several countries including Vietnam each year [M. F. Boni, B. H. Manh, P. Q. Thai, J. Farrar, T. Hien, N. T. Hien, N. Van Kinh and P. Horby, Modelling the progression of pandemic influenza A （H1N1） in Vietnam and the opportunities for reassortment with other influenza viruses, BMC Med. 7 （2009） 43, Doi： 10.1186/1741-7015-%43]. So it is important to study seasonal forces and factors which can affect the transmission of this disease. This paper studies an SIRS epidemic model with seasonal vaccination rate. This SIRS model has a unique disease-free solution （DFS）. The value Ro, the basic reproduction number is obtained when the vaccination is a periodic function. Stability results for the DFS are obtained when R0 〈 1. The disease persists in the population and remains endemic if R0 〉 1. Also when R0 〉 1 existence of a nonzero periodic solution is proved. These results obtained for our model when the vaccination strategy is a non-constant time-dependent function.
