A stability test for non linear systems of ordinary differential equations based on the Gershgorin circles

Bejarano, Danilo Alonso Ortega; Ibargüen-Mondragón, Eduardo; Gómez-Hernández, E. A.

doi:10.12988/ces.2018.89504

Cited by 13 publications

(5 citation statements)

References 12 publications

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“…Gershgorin stability theorem [4] states that the system will be stable if two conditions : J ii < 0 , and…”

Section: Stability Analysis Of Endemic Equilibriummentioning

confidence: 99%

Mathematical Analysis of Sveiqr Model for Covid-19

Kunwar¹,

Verma²

2023

SEAJMMS

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In this paper, we have proposed an SVEIQR compartmental model modifying the classical SEIR model with inclusion of vaccinated and quarantined classes to explain the COVID-19 outbreak mathematically. We have calibrated our model with the daily COVID-19 data reported by the WHO coronavirus dashboard. To observe the disease dynamics of COVID-19, a detailed stability analysis of the proposed SVEIQR model is carried out. Our results show that the disease free equilibrium (DFE) is stable if the basic reproduction number is less than unity and unstable otherwise. Moreover, endemic equilibrium (EE) is found to be stable when certain restrictions hold. The expression for effective reproduction number has been derived analytically and its value is calculated based on the reported cases. Sensitivity analysis of effective reproduction number is performed employing PRCCs and Latin hypercube scheme. We have compared short-term and long-term transmission dynamics of COVID-19 for India with different levels of vaccination and without control strategies. The impact of different degrees of control interventions is ascertained with the numerical simulation of the model.

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“…Gershgorin stability theorem [4] states that the system will be stable if two conditions : J ii < 0 , and…”

Section: Stability Analysis Of Endemic Equilibriummentioning

confidence: 99%

Mathematical Analysis of Sveiqr Model for Covid-19

Kunwar¹,

Verma²

2023

SEAJMMS

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“…(3.9) Following Gershgorin's circle theorem [8,32], the following inequalities are satisfied by matrix B…”

Section: Reproduction Numbermentioning

confidence: 99%

An epidemic model for control and possible elimination of Lassa fever

2023

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Lassa fever is a deadly viral disease whose incubation period ranges from six to twenty-one days and about eighty percent of Lassa virus infection is asymptomatic. A deterministic model was formulated to quantify the transmission dynamics of the disease under isolation and treatment of the isolated asymptomatic and symptomatic humans for effective management and possible elimination of the disease. The solutions of the model were shown to be positive and bounded. Equilibrium analysis was conducted and both the disease-free and the endemic equilibria were derived. The threshold quantity for disease elimination , $R_{0}$ , was also obtained and used to derive conditions for the existence of stability of the eqilibria. The quantity was also employed to examine the sensitivity of the model parameters to disease propagation and reduction. The theoretical analysis was then complemented with the quantitative analysis by adopting a set of realistic values for the model parameters in order to show the effect of isolation and treatment on the spread and fatality of Lassa fever. Results from the quantitative study showed that death and infection from Lassa fever fell continuously as more and more exposed individuals were detected and isolated for treatment. The study therefore suggested that any measure taken to eradicate or curtail Lassa fever spread should include detection and isolation of the exposed humans for prompt treatments.

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“…e equilibrium point can be either stable or unstable or a saddle point [26,27]. Gershgorin's theorem provides sufficient conditions for the eigenvalues to lie in the left half of the complex plane [25,[28][29][30]; that is, the local stability can be established without the need to calculate the eigenvalues, instead the basic reproduction number, which also gives a condition for an equilibrium point to be stable is used for the analysis, determines the sign of the constant term [24].…”

Section: Local Stability Analysis Of the Equilibrium Pointsmentioning

confidence: 99%

A Mathematical Model for Effective Control and Possible Eradication of Malaria

Adom-Konadu

Yankson

Naandam

et al. 2022

Journal of Mathematics

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In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies α and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort α was found to be the most sensitive parameter in the reduction of ℛ 0 . Hence, numerical simulations were performed using different values of α to determine an optimal value of α that reduces the incidence rate fastest. It was discovered that an optimal combination that reduces the incidence rate fastest comes from about 40 % of adherence to the preventive strategies coupled with about 40 % of infected humans seeking clinical treatment, as this will reduce the infected human and vector populations considerably.

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A stability test for non linear systems of ordinary differential equations based on the Gershgorin circles

Cited by 13 publications

References 12 publications

Mathematical Analysis of Sveiqr Model for Covid-19

Mathematical Analysis of Sveiqr Model for Covid-19

An epidemic model for control and possible elimination of Lassa fever

A Mathematical Model for Effective Control and Possible Eradication of Malaria

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