Stability analysis of an SIR epidemic model with homestead-isolation on the susceptible and infectious, immunity, relapse and general incidence rate

Abstract

In this paper, we propose the global dynamics of an SIR epidemic model with distributed latent period, immunity, relapse, homestead-isolation of the susceptible and infectious individuals and general incidence rate. The resulting model has a disease-free equilibrium and if [Formula: see text] then the SIR epidemic model admits a unique endemic equilibrium. By using suitable Lyapunov functionals and LaSalle’s invariance principle, the global stability of the disease-free equilibrium and the endemic equilibrium is established, under suitable monotonicity conditions on the incidence function.

Bifurcation Analysis for an OSN Model with Two Delays

“…Assume that R 0 > 1. Let a, b, c, d, and h be defined by (10), and a 1 , b 1 , and c 1 be defined by (13). Also let F, G be defined in (34) and (35).…”

“…Many of these models draw inspiration from SIR/SEIR disease-type models, providing a framework to study OSN dynamics effectively. Interested readers can delve into classic and advanced results on SIR/SEIR mathematical models and SIR/SEIR mathematical models with delays in works such as those by [12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein. Most recently, Barman and Mishra [25,26] introduced a graph Laplacian diffusion into SIR/SEIR type network models and carried out Hopf bifurcation analysis.…”