Tanzania on Monday became the latest east Africa country to confirm its first case of coronavirus, as neighbouring countries shuttered borders and schools as fears of contagion rose.

Health Minister Ummy Mwalimu said a 46-year-old Tanzanian woman had tested positive for the illness after returning from Belgium on March 15, and was recovering in a hospital in Arusha.

Mwalimu said the woman, who had been staying with someone sick from coronavirus in Belgium, was not detected by temperature scanners at the airport but reported herself for testing.

"All in all, this is an imported case, and the woman is improving and continues with treatment," she said, adding authorities would trace all the patient's contacts since she arrived in Tanzania, and place them under quarantine.

The announcement came as Rwanda confirmed four more cases of the virus, after reporting its first on Saturday.

According to a health ministry statement, the new cases include a 30-year-old Rwandan man "in Kigali with no travel history".

There is also a 34-year-old Rwandan man who arrived from South Sudan on March 6 and his brother who arrived from Fiji via the US and Qatar on March 8.

Fresh restrictions

The fourth patient is a 22-year-old Ugandan who arrived from London on March 15. They are all under treatment, isolated from other patients.

Rwanda has shut schools and churches for two weeks and banned concerts and large gatherings. Its national airline Rwandair has cancelled its flights to India, Israel and China.

Ethiopia introduced its own raft of fresh restrictions Monday, closing schools and suspending large gatherings like sporting events. The country, the most populous in the region with 100 million people, has five confirmed cases of coronavirus.

Mauritius, meanwhile, a smattering of islands in the Indian Ocean dependent on tourism, announced it would deny entry to anyone who had visited the EU, Switzerland or UK in the past 14 days.

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Previously, the restriction only applied to those who had visited China, Iran, Italy, South Korea and Hong Kong.

It has not recorded any positive cases so far.

"Our country is a tourist destination. Thousands of foreigners come to and transit through Mauritius. We are very exposed," said Prime Minister Pravind Jugnauth.

There are now 16 confirmed cases across five countries in east Africa.

Kenya, which has three cases, on Sunday announced strict measures including blocking entry to foreigners who do not have a valid resident permit and are coming from a country with a confirmed case.