scholarly journals Reproduction Numbers and the Stability of Equilibria of SI Models for Heterogeneous Populations

1992 ◽  
Vol 52 (2) ◽  
pp. 541-576 ◽  
Author(s):  
Carl P. Simon ◽  
John A. Jacquez
Keyword(s):  
Heterogeneous Populations ◽  
Stability Of Equilibria ◽  
Reproduction Numbers ◽  
The Stability

Threshold conditions for a family of epidemic dynamic models for malaria with distributed delays in a non-random environment

2018 ◽  
Vol 11 (06) ◽  
pp. 1850085 ◽  
Author(s):  
Divine Wanduku
Keyword(s):  
Incidence Rate ◽  
Dynamic Models ◽  
Family Type ◽  
Natural Immunity ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Reproduction Numbers ◽  
Threshold Conditions ◽  
Epidemic Dynamic ◽  
The Stability

A family of deterministic SEIRS epidemic dynamic models for malaria is presented. The family type is determined by a general functional response for the nonlinear incidence rate of the disease. Furthermore, the malaria models exhibit three random delays — the incubation periods of the plasmodium inside the female mosquito and human hosts, and also the period of effective acquired natural immunity against the disease. Insights about the effects of the delays and the nonlinear incidence rate of the disease on (1) eradication and (2) persistence of malaria in the human population are obtained via analyzing and interpreting the global asymptotic stability results of the disease-free and endemic equilibrium of the system. The basic reproduction numbers and other threshold values for malaria are calculated, and superior threshold conditions for the stability of the equilibria are found. Numerical simulation results are presented.

Stability and Bifurcation in an SI Epidemic Model with Additive Allee Effect and Time Delay

2021 ◽  
Vol 31 (04) ◽  
pp. 2150060
Author(s):  
Yangyang Lv ◽  
Lijuan Chen ◽  
Fengde Chen ◽  
Zhong Li
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Allee Effect ◽  
Stability Of Equilibria ◽  
Existence And Stability ◽  
Vital Effects ◽  
Strong Allee Effect ◽  
The Stability

In this paper, we consider an SI epidemic model incorporating additive Allee effect and time delay. The primary purpose of this paper is to study the dynamics of the above system. Firstly, for the model without time delay, we demonstrate the existence and stability of equilibria for three different cases, i.e. with weak Allee effect, with strong Allee effect, and in the critical case. We also investigate the existence and uniqueness of Hopf bifurcation and limit cycle. Secondly, for the model with time delay, the stability of equilibria and the existence of Hopf bifurcation are discussed. All the above show that both additive Allee effect and time delay have vital effects on the prevalence of the disease.

scholarly journals The stability of equilibria under selection

Heredity ◽  
1971 ◽  
Vol 27 (2) ◽  
pp. 157-162 ◽  
Author(s):  
M G Bulmer
Keyword(s):  
Stability Of Equilibria ◽  
The Stability
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