Well then. It's easy to replicate their "model"; all you need is a ginormous diamond mine.
I was a Peace Corps volunteer there in the late 1980s, and saw a lot of schools and health clinics built by the government, roads extended, water pumps installed, and so on. They also had adult education centers set up in many villages.
I went to teach there after a planned group of volunteers for Zaire fell through (for political reasons). The government of Botswana found out and told Peace Corps to send all the math/science teachers they could. I think that speaks to the mindset of the governance there.
Another aspect of the lack of corruption was the day-to-day interactions with authorities. In Zimbabwe or Kenya, if your bus got pulled over by the police it was always for a bribe. In Botswana, a group of soldiers would empty out the bus of passengers, inspect everything (no doubt looking for bombs and other arms related to the resistance to apartheid in neighboring South Africa), and then let you get back on the bus. Not a jot of personal property would be touched, nor money change hands, as far as I ever saw.
Finally, the Batswana culture always seemed to me to be incredibly peaceful, for want of a better word. My sense (not an anthropologist by any means) is that Botswana has a culture very much like an extended farm village. Most people live off the land, and the population is very sparse. Unless you're in a pretty large city (and there are maybe two or three), you simply don't walk past somebody without saying hello (and following a prescribed ritual for doing so). Even in the capital, you tend to acknowledge people as you pass them. There were of course problems, but in general I never feared to walk around anywhere, or to talk with anybody.
Levitsky and Way, in Competitive Authoritarianism, (https://books.google.com/books?hl=en&lr=&id=NZDI05p1PDgC&oi=...) describe it as a stable authoritarian government. Although the country does hold nominally competitive elections, the Botswana Democratic Party (BDP) has held power since they gained independence. That the country's diamond industry has thrived over the last 40 years is no coincidence.
A valid point, but not entirely fair. The diamonds contribute but its seen as a legitimately well run country in its own right - well by African standards anyway.