scholarly journals An SEIR model with infected immigrants and recovered emigrants

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Peter J. Witbooi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Positive Solutions ◽  
Equilibrium Points ◽  
Local Population ◽  
Asymptotically Stable ◽  
Short Stay ◽  
Seir Model ◽  
Threshold Levels

AbstractWe present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. In particular, the model allows for a constant inflow of individuals into different classes and constant outflow of individuals from the R-class. The system of ordinary differential equations has positive solutions and the infected classes remain above specified threshold levels. The equilibrium points are shown to be asymptotically stable. The utility of the model is demonstrated by way of an application to measles.

On the asymptotic behaviour of nonlinear systems of ordinary differential equations

1985 ◽  
Vol 26 (2) ◽  
pp. 161-170
Author(s):  
Zhivko S. Athanassov
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Ordinary Differential Equations ◽  
Asymptotically Stable ◽  
Future Time ◽  
Zero Function ◽  
Perturbed Systems ◽  
Approach Zero ◽  
Image Position

In this paper we study the asymptotic behaviour of the following systems of ordinary differential equations:where the identically zero function is a solution of (N) i.e. f(t, 0)=0 for all time t. Suppose one knows that all the solutions of (N) which start near zero remain near zero for all future time or even that they approach zero as time increases. For the perturbed systems (P) and (P1) the above property concerning the solutions near zero may or may not remain true. A more precise formulation of this problem is as follows: if zero is stable or asymptotically stable for (N), and if the functions g(t, x) and h(t, x) are small in some sense, give conditions on f(t, x) so that zero is (eventually) stable or asymptotically stable for (P) and (P1).

DYNAMICS OF NUMERICAL METHODS FOR COSYMMETRIC ORDINARY DIFFERENTIAL EQUATIONS

2001 ◽  
Vol 11 (09) ◽  
pp. 2339-2357 ◽  
Author(s):  
V. N. GOVORUKHIN ◽  
V. G. TSYBULIN ◽  
B. KARASÖZEN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Equilibrium Points ◽  
Two Dimensions ◽  
Model Systems ◽  
Continuous Family ◽  
First Order ◽  
Spurious Solutions ◽  
Overall Performance ◽  
The Stability

The dynamics of numerical approximation of cosymmetric ordinary differential equations with a continuous family of equilibria is investigated. Nonconservative and Hamiltonian model systems in two dimensions are considered and these systems are integrated with several first-order Runge–Kutta methods. The preservation of symmetry and cosymmetry, the stability of equilibrium points, spurious solutions and transition to chaos are investigated by presenting analytical and numerical results. The overall performance of the methods for different parameters is discussed.

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