In this paper,we study a network-based SIR epidemic model with a saturated treatment function in which a parameterαis introduced to measure the extent of the effect of the infected being delayed for treatment.Our aim...In this paper,we study a network-based SIR epidemic model with a saturated treatment function in which a parameterαis introduced to measure the extent of the effect of the infected being delayed for treatment.Our aim is to present a global analysis and to investigate how the parameterαaffects the spreading of diseases.Our main results are as follows:(1)In the case of the threshold value R_(0)<1,there exist two values of α:α_(c) and α_(0),such that the disease-free equilibrium is globally asymptotically stable when α≤α_(0) and multiple endemic equilibria exist when α≥α_(0).This means that the parameterαhas an essential infuence on the spreading of the disease.(2)In the case of the threshold value R_(0)>1,if the model has only one endemic equilibrium,then the unique endemic equilibrium is globally attractive.In this case,it is also proved that if α≤α_(c),then the endemic equilibrium has only one,so is globally attractive,In addition,numerical simulation is performed to illustrate our theoretical results.展开更多
An SIS epidemic model with the standard incidence rate and saturated treatment func- tion is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the ...An SIS epidemic model with the standard incidence rate and saturated treatment func- tion is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the population are also studied. We find that the effect of the maximum recovery per unit of time and the recruitment rate of the popula- tion over some level are two factors which lead to the backward bifurcation, and in some cases, the model may undergo the saddle-node bifurcation or Bogdanov-Takens bifurca- tion. It is shown that the disease-free equilibrium is globally asymptotically stable under some conditions, Numerical simulations are consistent with our obtained results in the- orems, which show that improving the efficiency and capacity of treatment is important for control of disease.展开更多
A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into ...A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function,which caters for high saturation of onchocerciasis disease.We analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix method.Also,we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if R_(hb) is less than unity,the onchocerciasis-free equilibrium is locally and globally asymptotically stable.Furthermore,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than unity.In addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the model.Graphical results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease menace.Further simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.展开更多
基金The research was supported in part by the NNSFC(grant 12071058)the Applied Basic Research Program of Department of Science and Technology of Liaoning Province of China(grant 2023JH2/101300095).
文摘In this paper,we study a network-based SIR epidemic model with a saturated treatment function in which a parameterαis introduced to measure the extent of the effect of the infected being delayed for treatment.Our aim is to present a global analysis and to investigate how the parameterαaffects the spreading of diseases.Our main results are as follows:(1)In the case of the threshold value R_(0)<1,there exist two values of α:α_(c) and α_(0),such that the disease-free equilibrium is globally asymptotically stable when α≤α_(0) and multiple endemic equilibria exist when α≥α_(0).This means that the parameterαhas an essential infuence on the spreading of the disease.(2)In the case of the threshold value R_(0)>1,if the model has only one endemic equilibrium,then the unique endemic equilibrium is globally attractive.In this case,it is also proved that if α≤α_(c),then the endemic equilibrium has only one,so is globally attractive,In addition,numerical simulation is performed to illustrate our theoretical results.
文摘An SIS epidemic model with the standard incidence rate and saturated treatment func- tion is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the population are also studied. We find that the effect of the maximum recovery per unit of time and the recruitment rate of the popula- tion over some level are two factors which lead to the backward bifurcation, and in some cases, the model may undergo the saddle-node bifurcation or Bogdanov-Takens bifurca- tion. It is shown that the disease-free equilibrium is globally asymptotically stable under some conditions, Numerical simulations are consistent with our obtained results in the- orems, which show that improving the efficiency and capacity of treatment is important for control of disease.
文摘A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function,which caters for high saturation of onchocerciasis disease.We analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix method.Also,we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if R_(hb) is less than unity,the onchocerciasis-free equilibrium is locally and globally asymptotically stable.Furthermore,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than unity.In addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the model.Graphical results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease menace.Further simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.
