Corona Virus in Lithuania

Population of Corona Virus infected people in Lithuania started to grow on the second week of March. Here you have an excerpt from the official report:

UPDATE March $13$:

As of the $13$th of March, Three new coronavirus $($COVID$-19)$ cases have been confirmed.

One of the cases concerns a Spanish national, a woman from Madrid. The other two are Lithuanians. A woman in Klaipeda tested positive after returning from Tenerife in the Canary Islands. A man in Kaunas has also been diagnosed following a skiing trip to Italy.

To date, $6$ cases of coronavirus $($COVID$-19)$ confirmed in Lithuania.

Use the population growth model

$P(t)=\frac{L}{1+e^{R(C-t)}}$

to forecast the number of cases for the first $5$ days of April.

Here you have the table of virus spread data to calibrate the model.

Total amount of confirmed COVID$-19$ cases in Lithuania

Table

$($Day $5-20200313)$

$\backslash$table$[[$Day$,5,6,7,8,9,10,11,12,13,14],[$Confirmed Cases,$6,9,12,14,22,33,48,63,99,143],[$Day$,15,16,17,18,19,20,21,22,23,],[$Confirmed Cases,$179,209,255,290,358,382,460,484,533,]]$

Make another forecast ignoring data from days $5-13,$ when number of tests performed was limited by the reagents availability.

Illustrate both cases with charts.