Bifurcation analysis of a network-based SIR epidemic model with saturated treatment function

Li, Chun-Hsien; Yousef, A. M.

doi:10.1063/1.5079631

Cited by 36 publications

(18 citation statements)

References 29 publications

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“…The limitation of medical supply may lead to a saturation phenomenon; that is, during severe disease outbreaks the number of patients who need to be treated may exceed the treatment capacity so that the number of patients who receive treatment will reach a saturation level. Saturated treatment function is used and explained in details in [12,16,21,34,35,36].…”

Section: A Mathematical Modelmentioning

confidence: 99%

Modelling the Transmission Dynamics of Contagious Bovine Pleuropneumonia in the Presence of Antibiotic Treatment With Limited Medical Supply

Aligaz

Munganga

2021

Mathematical Modelling and Analysis

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We present and analyze a mathematical model of the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) in the presence of antibiotic treatment with limited medical supply. We use a saturated treatment function to model the effect of delayed treatment. We prove that there exist one disease free equilibrium and at most two endemic equilibrium solutions. A backward bifurcation occurs for small values of delay constant such that two endemic equilibriums exist if Rt (R*t,1); where, Rt is the treatment reproduction number and R*t is a threshold such that the disease dies out if and persists in the population if Rt > R*t. However, when a backward bifurcation occurs, a disease free system may easily be shifted to an epidemic. The bifurcation turns forward when the delay constant increases; thus, the disease free equilibrium becomes globally asymptotically stable if Rt < 1, and there exist unique and globally asymptotically stable endemic equilibrium if Rt > 1. However, the amount of maximal medical resource required to control the disease increases as the value of the delay constant increases. Thus, antibiotic treatment with limited medical supply setting would not successfully control CBPP unless we avoid any delayed treatment, improve the efficacy and availability of medical resources or it is given along with vaccination.

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Section: A Mathematical Modelmentioning

confidence: 99%

Modelling the Transmission Dynamics of Contagious Bovine Pleuropneumonia in the Presence of Antibiotic Treatment With Limited Medical Supply

Aligaz

Munganga

2021

Mathematical Modelling and Analysis

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“…For examples on the use of the saturated treatment function in epidemiological modelling, we refer to [40][41][42].…”

Section: Control Problem Statementmentioning

confidence: 99%

Set-Valued Control Approach Applied to a COVID-19 Model with Screening and Saturated Treatment Function

et al. 2020

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The purpose of this paper is modelling and controlling the spread of COVID-19 disease in Morocco. A nonlinear mathematical model with two subclasses of infectious individuals is proposed. The population is divided into five classes, namely, susceptible (S), exposed (E), undiagnosed infectious ( I n c ), diagnosed patients ( I c ), and removed individuals. To reflect the real dynamic of the COVID-19 transmission in Morocco, the real reported data are used for estimating model parameters. Two controls representing screening effort and limited treatment are considered. Based on viability theory and set-valued analysis, a Lyapunov function is constructed such that both exposed and infected populations are decreased to zero asymptotically. The corresponding controls are derived via a continuous selection of adequately designed feedback map. Numerical simulations are presented with three scenarios (cases when each control is used alone and the case when two controls are combined). Our results show that when only one control is to be applied, screening is the most effective in decreasing the number of people in the three infected compartments, whereas combining both controls is found to be highly effective and leads to a significant improvement in the epidemiological situation of Morocco. To the best of our knowledge, this work is the first one that applies the set-valued approach to a controlled COVID-19 model which agrees with the observed cases in Morocco.

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“…Recently, Li and Yousef proposed two degree-based SIR and SIS models with a saturated function to study a backward bifurcation phenomena. They showed a sufficient condition for the occurrence of a backward bifurcation [23,24]. Indeed, since network models have higher dimensions than those of well-mixed models, studying the complex dynamics of such models is a challenging issue from a theoretical view of points.…”

Section: Introductionmentioning

confidence: 99%

A Bistable Phenomena Induced by a Mean-Field SIS Epidemic Model on Complex Networks: A Geometric Approach

Wang

Yang

2021

Front. Phys.

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In this paper, we propose a degree-based mean-field SIS epidemic model with a saturated function on complex networks. First, we adopt an edge-compartmental approach to lower the dimensions of such a proposed system. Then we give the existence of the feasible equilibria and completely study their stability by a geometric approach. We show that the proposed system exhibits a backward bifurcation, whose stabilities are determined by signs of the tangent slopes of the epidemic curve at the associated equilibria. Our results suggest that increasing the management and the allocation of medical resources effectively mitigate the lag effect of the treatment and then reduce the risk of an outbreak. Moreover, we show that decreasing the average of a network sufficiently eradicates the disease in a region or a country.

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Bifurcation analysis of a network-based SIR epidemic model with saturated treatment function

Cited by 36 publications

References 29 publications

Modelling the Transmission Dynamics of Contagious Bovine Pleuropneumonia in the Presence of Antibiotic Treatment With Limited Medical Supply

Modelling the Transmission Dynamics of Contagious Bovine Pleuropneumonia in the Presence of Antibiotic Treatment With Limited Medical Supply

Set-Valued Control Approach Applied to a COVID-19 Model with Screening and Saturated Treatment Function

A Bistable Phenomena Induced by a Mean-Field SIS Epidemic Model on Complex Networks: A Geometric Approach

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