Three kinds of TVS in a SIR epidemic model with saturated infectious force and vertical transmission

Qualitative and Bifurcation Analysis of an SIR Epidemic Model with Saturated Treatment Function and Nonlinear Pulse Vaccination

“…However, impulsive differential equations [6,7] are also suitable for the mathematical simulation of evolutionary processes in which the parameters state variables undergo relatively long periods of smooth variation followed by a short-term rapid change in their values. Many results have been obtained for SIR epidemic models described by impulsive differential equations [8][9][10][11][12][13].…”

Two patterns of recruitment in an epidemic model with difference in immunity of individuals

“…In particular, some authors have studied the effects of vaccination on the spread of diseases [2][3][4][5][6][7][8][9][10][11]; some authors have studied the effects of treatment on the spread of diseases [12][13][14][15]; Gao et al have proposed an epidemic model with density-dependent birth pulses and seasonal prevention [16]; recently, some works have investigated permanent and temporary immunity [17][18][19][20][21][22]27]. One of the unrealistic assumptions in these works, is that all the infected individuals except those who die acquire immunity.…”

“…Various epidemic models have been formulated and analyzed in [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In particular, some authors have studied the effects of vaccination on the spread of diseases [2][3][4][5][6][7][8][9][10][11]; some authors have studied the effects of treatment on the spread of diseases [12][13][14][15]; Gao et al have proposed an epidemic model with density-dependent birth pulses and seasonal prevention [16]; recently, some works have investigated permanent and temporary immunity [17][18][19][20][21][22]27].…”

Switching Vaccination Schemes for Vector-Borne Diseases With Seasonal Fluctuations

“…Cohort immunization that is applied continuously to a population has been extensively studied in the literature. 21,[30][31][32][33] Pulse vaccination, which has gained prominence in recent years for achieving disease eradication at lower vaccination levels than conventional time-constant control, 34 was first proposed by Shulgin et al in Ref. 34 and has since been further developed, for example, in Refs.…”