In Zimbabwe, the long and fairly tortured process of drafting a new constitution appears to have ended. The various parties have agreed a text. MPs have approved the draft text. A referendum is scheduled to be held later in the year for voters to decide whether or not to adopt it. The text of the draft constitution is available here.
As has been rumoured for some time now, the draft constitution is presidential-like. The president is directly elected (Art. 92) and is both head of state and government (Art. 89). The president and parliament both serve for a five-year term (Art. 95). There is a cabinet, but there is no prime minister. The president can dismiss ministers individually and collectively (Arts. 107 and 108). However, the legislature can also vote no-confidence in the government collectively. In this event, the president either appoints a new government or there is a general election (Art. 109). The president may also dissolve parliament under certain circumstances (Art. 143). Parliament may also under certain circumstances vote its own dissolution. Crucially, if parliament is dissolved, then there is both a presidential and a parliamentary election (which is called a general election). So, the presidential and parliamentary terms are not fully fixed.
Overall, the system seems to be like the one in Zambia if I am not mistaken. This is a very close variant of a presidential system.