Donner le point d'équilibre endémique du système d'équations différentielles résolu simultanément:
dS/dt = μN + ∆ - βS*I - ℇ1*T1*S + υ*V1 - γ*S - ℇ1*Tvm*S + ρ*V2
dV1/dt = ℇ1*T1*S - ℇ2*T2*V1 - γ*V1 - υ*V1
dV2/dt = ℇ2*T2*V1 - ρ*V2 - γ*V2 - δ*V2
dVm/dt = ℇ1*Tvm*S - Ƞ*Vm - γ*Vm
dE/dt = β*S*I - α*E - γ*E
dI/dt = α*E + Ƞ*Vm - θ*I - γ*I + φ*I
dR/dt = θ*I + δ*V2 - γ*R

To find the endemic equilibrium point of the given system of differential equations, we need to set each of the derivatives equal to zero and solve the resulting system of algebraic equations for the steady-state values of the variables \( S, V1, V2, Vm, E, I, R \). The endemic equilibrium corresponds to a situation where the disease persists in the population, meaning \( I \neq 0 \).

The system of differential equations provided is:

\[
\begin{align*}
\frac{dS}{dt} &= \mu N + \Delta - \beta SI - \epsilon_1 T_1 S + \nu V_1 - \gamma S - \epsilon_1 T_{vm} S + \rho V_2 \\
\frac{dV_1}{dt} &= \epsilon_1 T_1 S - \epsilon_2 T_2 V_1 - \gamma V_1 - \nu V_1 \\
\frac{dV_2}{dt} &= \epsilon_2 T_2 V_1 - \rho V_2 - \gamma V_2 - \delta V_2 \\
\frac{dV_m}{dt} &= \epsilon_1 T_{vm} S - \eta V_m - \gamma V_m \\
\frac{dE}{dt} &= \beta SI - \alpha E - \gamma E \

Explore the endemic equilibrium point of a system of differential equations in epidemiology. Learn how to find steady-state solutions for variables like S, V1, V2, Vm, E, I, and R. This problem involves complex mathematical modeling and is suitable for advanced undergraduate studies.

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