I am working with an epidemiological model in the form of a dynamical system of seven ODEs and I am trying to show that the DFE is stable if R0<1. When applying the Routh-Hurwitz criterion, I see that one of the coefficients of the characteristic polynomial cannot be rewritten in terms of R0 (so that the coefficient is positive when R0<1). I tried to manipulate this coefficient in several ways, but end up getting another condition for that coefficient to be positive apart from R0<1. So, I just wanted to know if this is allowed or if I am doing something wrong. Also, I want to confirm that I checked my computations and simplifications several times, so I am certain that I am not doing any simplification errors. Thank you for your time!
2026-03-25 19:11:46.1774465906
Stability Analysis of DFE in terms of R0 Using Ruth-Hurwitz Criterion
59 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ORDINARY-DIFFERENTIAL-EQUATIONS
- The Runge-Kutta method for a system of equations
- Analytical solution of a nonlinear ordinary differential equation
- Stability of system of ordinary nonlinear differential equations
- Maximal interval of existence of the IVP
- Power series solution of $y''+e^xy' - y=0$
- Change of variables in a differential equation
- Dimension of solution space of homogeneous differential equation, proof
- Solve the initial value problem $x^2y'+y(x-y)=0$
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Derive an equation with Faraday's law
Related Questions in EIGENVALUES-EIGENVECTORS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Show that this matrix is positive definite
- Is $A$ satisfying ${A^2} = - I$ similar to $\left[ {\begin{smallmatrix} 0&I \\ { - I}&0 \end{smallmatrix}} \right]$?
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Question on designing a state observer for discrete time system
- Evaluating a cubic at a matrix only knowing only the eigenvalues
- Eigenvalues of $A=vv^T$
- A minimal eigenvalue inequality for Positive Definite Matrix
- Construct real matrix for given complex eigenvalues and given complex eigenvectors where algebraic multiplicity < geometric multiplicity
Related Questions in STABILITY-IN-ODES
- Stability of system of ordinary nonlinear differential equations
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- How to analyze a dynamical system when $t\to\infty?$
- The system $x' = h(y), \space y' = ay + g(x)$ has no periodic solutions
- Existence of unique limit cycle for $r'=r(μ-r^2), \space θ' = ρ(r^2)$
- Intuitive proof of Lyapunov's theorem
- Stability of a nonlinear ODE system (only existence of the limit)
- Deriving inequality from a Lyapunov test of $x' = -x + y^3, \space y' = -y + ax^3$
- does the order lineariztion/evaluation matter here?
Related Questions in BIOLOGY
- Calculating half life from proteins
- How Turing instability explains the patterns present on the animal skin?
- Mutation probability
- biology models which uses a system of differential equations
- basic reproduction number using next generation matrix
- Lyapunov function for predator-prey system
- How to convert a detailed mathematical, statistical compuational process into mathematical and statistical equation?
- Relationship between graphs describing horizontal and vertical cell network
- How to calculate $r<r_{c} $?
- How to analyse u as s evolves across different values?
Related Questions in MATHEMATICAL-BIOLOGY
- An alternative to the popular Hutchinson population model
- Showing an endemic steady state is stable
- How do I calculate the equilibria, rate of production of infected cells, average lifespan of infected cells and basic reproduction number?
- persistence of SEIR epidemic model
- Recovery Time for Logistic model equation with harvesting
- 3 species Lotka–Volterra model. Limit cycle
- Traveling-wave solution for McKendrick age-structure model with finite lifespan
- Help Finding a Traveling Wave Solution
- Adjusting death rate based on known half-life
- Reaction Diffusion Equation general solution
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?