This paper addresses a time-delayed SIQRS model with a linear incidence rate. Immunity gained by experiencing the disease is temporary; whenever infected, the disease individuals will return to the susceptible class after a fixed period of time. First, the local and global stabilities of the infection-free equilibrium are analyzed, respectively. Second, the endemic equilibrium is formulated in terms of the incidence rate, and locally asymptotic stability. Finally we use the adomian decomposition method is applied to the system epidemiologic. This method yields an analytical solution in terms of convergent infinite power series.
It is our intention, in this chapter, to propose and discuss the Best Payoff Method, a new method to resolve games. This is made exemplifying the application of the method to a pay raise voting game, that is a perfect information sequential game, without having yet formulated it, and then deploying the algorithm for its implementation. In the next examples we consider an imperfect information game and a game with random characteristics. We finish confronting the equilibrium concepts mentioned in this work: Subgame Perfect Nash Equilibrium, Nash Equilibrium, and Best Payoff Equilibrium through the formulation of some conjectures, and with a short conclusions section.
In this work, we consider a multicompartment nonlinear epidemic model with temporary immunity and a saturated incidence rate. N(t) at time t, this population is divide into seven sub-classes. N(t) = S(t) + E(t) + I(t) + I1(t) + I2(t) + I3(t) + Q(t). where S(t),E(t); I(t); I(t); I1(t),I2(t); I3(t) and Q(t) denote the sizes of the population susceptible to disease, exposed, infectious members and quarantine members with the possibility of infection through temporary immunity, respectively.The stability of a disease-free status equilibrium and the existence of endemic equilibrium determined by the ratio called the basic reproductive number. The multicompartment non linear epidemic model with saturated rate has been studied the stochastic stability of the free disease equilibrium under certain conditions, and obtain the conditions of global attractivity of the infection.
In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.
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