Here are some thoughts on how "lockdowns" function in the 3rd World. In the absence of widespread laboratory testing a lockdown is a proxy method of detection.
The carriers amplify their presence by becoming locally obvious and standing out. It's like a petrie dish where the organisms become visible in the culture allowing the authorities to localize the contact and depth-charge them with countermeasures.
You do this when you have no better way of finding the infected. Any lockdown strategy crucially requires an information gathering and processing component without which it is largely pointless. Your hidden markov model is never solved and no benefit is obtained.
China had very extensive mass surveillance and data processing capabilities. They could "see" the hot spots in the petrie dish and deal with it ruthlessly. Ditto South Korea.
Without a similar ability what could result is a Cargo Cult lockdown imitating the forms but totally missing the essence. The most important output of a lockdown is information. This should be obvious but it may be overlooked.
So some lockdowns are going to help but those without the crucial info analysis component may actually make it worse.
