The effects of the functional response on the bifurcation behavior of a mite predator-prey interaction model

1997 ◽  
Vol 36 (2) ◽  
pp. 149-168 ◽  
Author(s):  
John B. Collings
Keyword(s):  
Functional Response ◽  
Interaction Model ◽  
Predator Prey ◽  
Prey Interaction ◽  
Mite Predator ◽  
Bifurcation Behavior

scholarly journals Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Getachew Bitew Birhan ◽  
Justin Manango W. Munganga ◽  
Adamu Shitu Hassan
Keyword(s):  
Cystic Echinococcosis ◽  
Transmission Rate ◽  
Interaction Model ◽  
Transmission Dynamics ◽  
Human Populations ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Prey Interaction ◽  
Disease Free

In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number R 0 and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if R 0 > 1 . We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if R 0 < 1 . Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep ( β es ). Thus, the effective controlling strategies are associated with this parameter.

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