Sentence examples for both equations of model from inspiring English sources

Both equations of model (18) are nonlinear, but with a similar term β μ S ( t ) I ( t ) Λ.

For validation, both the analytic solutions and the differential equations of models A D are fitted and S t) set to always be greater than zero, ensuring physically realistic results.

From the second equation of model (21) we know that θ ( t ) is always constant.

From the fourth equation of model (2) we further have (lim_{ntoinfty}R(n)=0).

According to the third equation of model (7), we have (v_{1}=frac{v_{0}+phi ky_{1}}{1+phi u}).

When (I(n)equiv0), from the third equation of model (2) we have (E(n)equiv0).

From the first equation of model (2) we also have (lim_{ntoinfty}S(n)=S_{0}).

The first equation of model (17) is independent of other two state variables S ( t ) and I ( t ).

Further the second equation of model (2.4) shows that (lim_{nrightarrowinfty}E(n)=:E^) exists and (E^=frac{mu+k_{3}}{k_{2}}I^).

end{aligned} Owing to (z_{1}>0), from the last equation of model (7) we have (y_{1}<frac{1+phi b}{phi c}).

By the fourth equation of model (2) we further have that (R(n+1)) exists and (R(n+1)>0).