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DYNAMICS OF SIS EPIDEMIC MODEL WITH THE STANDARD INCIDENCE RATE AND saturated treatment function

International Journal of Biomathematics 2012年第3期5卷 43-60页

作者： JINGJING WEI JING-AN CUI Nanjing University of Science and Technology Zijin College Nanjing 210046 Jiangsu P. R. China School of Science Beijing Universityof Civil Engineering and Architecture Beijing 100044 P. R. China

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.

关键词： SIS epidemic model saturated treatment function backward bifurcation stability.

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Transmission dynamics of onchocerciasis with two classes of infection and saturated treatment function

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第5期11卷 184-207页

作者： Amos Sesan Idowu Oluwatayo Michael Ogunmiloro Department of Mathematics Faculty of Physical Science University of IlorinIlorinKwara StateNigeria Department of MathematicsFaculty of Science Ekiti State UniversityAdo-EkitiEkiti StateNigeria Oluwatayo Michael

A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is *** 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 *** analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix ***,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 ***,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than *** addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the *** results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease *** 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.

关键词： Onchocerciasis saturated treatment function basic reproduction number stability analysis

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