Local health departments ask for patience as they work through appointments for second COVID-19 vaccine doses Coronavirus vaccine demand, waitlisting raises concerns for some Houstonians Nearly 2 million Texans have already received at least one dose of the COVID-19 vaccine but the vaccine is still in high demand Local health departments urge patience as they work to get second doses into arms. City of Houston "It seems like a long time, but it's really only been a month since we started getting weekly shipments," said Porfirio Villareal, spokesperson, Houston Health Department. He adds those needing their second dose will get a call within two days of when they're due for their next shot.