Global dynamics and bifurcation in delayed SIR epidemic model

Stability analysis of delay seirepidemic model

“…depending on present values and some previous values of the state variables. Many authors used this variable in their model such as D 'Onofrio et al (2007), D 'Onofrio, Manfredi (2007), Buonomo et al (2008), Kar and Mondal (2011). We take the formula (Eq.…”

“…The work of Kar and Mondal (2011) motivated us for current study, and incorporated the E(t) (exposed Class) to our new model, and studying the model with the new information variable. By incorporating this class, the analysis of SEIR model with information variable will be more interesting for readers and researchers.…”

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

“…[15,[21][22][23][24]. Similarly some authors [25][26][27][28][29] used the rate of incidence in the form aSI 1 + bI . In this form of incidence the increase in the number of infected population increases the incidence term and it ultimately becomes proportional to the number of susceptible populations.…”

“…The term like 1+bI in the denominator of the incidence term measures the inhibition effect from the behavioral change of the susceptible individuals when the number of infectious individuals increases or from the crowding effect of the infective individuals [30] . Kar and Mondal [25] used the saturation effect in the form pSI 1 + αS , where α was defined as the half saturation constant. Here with the increase of the susceptible population the incidence term will increase and it ultimately becomes proportional to the number of infected individuals.…”

Global dynamics of a delayed SEIS infectious disease model with logistic growth and saturation incidence

“…Following the work of Anderson and May , in , Kar and Mondal considered the following SIR epidemic model with a saturation incidence: where the parameters r , α , β , γ 1 , μ 1 , μ 2 and K are positive constants. Model is established under the following assumptions: The susceptible population in the community under consideration satisfies the logistic growth; r is the intrinsic growth rate of susceptible populations; K is the carrying capacity of susceptible population. β represents the infectious transmission rate (average number of contacts per infective per day); β S I measures the infection force of the disease and 1/(1 + α S ) measures the inhibition effect from the behavioral change of the susceptible individuals. μ 1 and μ 2 are the per capita death rates of infectives and the recovered, respectively.…”