Positivity of compartments in epidemiological model

[kalish1]

Given the following dynamical model (system of ODEs):

\begin{array}
$
\frac{dA}{dt}=\Lambda-\mu A-\beta(C+D+E+F)\frac{A}{N}-\tau(B+D)\frac{A}{N} \\
\frac{dB}{dt}=\tau(B+D)\frac{A}{N}-\beta(C+D+E+F)\frac{B}{N}-(\mu+\mu_T)B, \\
\frac{dC}{dt}=\beta(C+D+E+F)\frac{A}{N}-\tau(B+D)\frac{C}{N}-(\mu+\mu_A)C, \\
\frac{dD}{dt}=\beta(C+D+E+F)\frac{B}{N}+\tau(B+D)\frac{C}{N}-(\mu+\mu_T+\mu_A+\lambda_T)D, \\
\frac{dE}{dt}=\lambda_TD-(\mu+\mu_A+\rho_1+\eta_1)E, \\
\frac{dF}{dt}=\rho_1E-(\mu+\mu_A+\rho_2+\eta_2)F, \\
\frac{dG}{dt}=\eta_1E-(\mu+\rho_1+\gamma)G, \\
\frac{dH}{dt}=\eta_2H+\rho_1G-(\mu+\rho_2+\frac{\gamma\rho_1}{\rho_1+\rho_2})H, \\
%,$
\end{array}

where $\mu, \beta, \tau, \mu_T, \mu_A, \gamma, \lambda_T, \eta_1, \eta_2, \rho_1, \rho_2 >0 \\$ and $A(0), B(0), C(0), D(0), E(0), F(0), G(0), H(0)>0,$

is it possible to show simply that $A(t),B(t),C(t),D(t),E(t),F(t),G(t),H(t) > 0?$

Or should I follow sections $II$ (Mathematical Formulation) and $III$ (Methodology) in this paper: http://www.iosrjournals.org/iosr-jm/papers/Vol5-issue5/G0554652.pdf

?

I have crossposted this question here: http://math.stackexchange.com/questions/1106786/positivity-of-compartments-in-epidemiological-model

 

[jvicens]

s

it is important to follow proper methodology in order to ensure the validity and accuracy of your findings. In this case, it would be best to follow the sections outlined in the paper you have referenced in order to analyze the dynamics of the system of ODEs and determine the positivity of the compartments.

Section II of the paper discusses the mathematical formulation of the model, which includes defining the variables, parameters, and initial conditions. This step is crucial in understanding the model and its behavior.

Section III outlines the methodology for analyzing the system of ODEs. This includes stability analysis, which is important in determining the behavior of the model over time. By analyzing the stability of the model, you can determine whether the compartments will remain positive or if they will eventually approach zero.

Additionally, it may be helpful to plot the solutions of the system of ODEs over time to visually see the behavior of the compartments. This can aid in determining the positivity of the compartments.

In conclusion, while it may be possible to show the positivity of the compartments in this model simply, it is important to follow proper methodology in order to ensure the accuracy of your results. Therefore, it would be best to follow the sections outlined in the paper and thoroughly analyze the system of ODEs in order to determine the positivity of the compartments.