Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology

Abstract

In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For [Formula: see text], the disease-free equilibrium is stable both locally and globally and for [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented.

Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

“…where is defined in (8) and ( , 0 ) is the unique solution of system (7) with (0, 0 ) = 0 . We define the following sets:…”

“…Multiple types of saturated incidence have been used in the literature; see, for example, [2] for a list of them. To avoid the use of a single incidence function, the use of a general incidence rate that includes a family of particular functions with similar properties has become a topic of interest by several authors (see, e.g., [4][5][6][7][8]). …”

An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model

“…Following the idea of [ 20 , 36 , 37 ], let us denote and , so . By the first equation of model ( 2.2 ), it can be seen that , which can be recast as Integrating the equality above from 0 to yields and then one obtains Therefore, for all .…”

Numerical analysis of stochastic SIR model by Legendre spectral collocation method

“…These models have been proposed by many researchers to study the dynamics of disease spread and controls. [1][2][3][4][5][6][7][8][9] Mathematical modeling of infectious diseases has an old history. In 1760, an infectious disease model was proposed by Bernoulli 10 for smallpox.…”