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It isn't appropriate to say whether the corona virus is man-made or not without clear evidence.

However, one can also consider a third option - namely, not all acts of God are punishment, even if they involve destruction. We learn from the Qur'an, such as the story of Khidr (A), that sometimes things that seem evil are actually for the greater good. Also, it is good to remember that there have been plagues throughout most of human history, so it isn't something new; it is only because we have become accustomed to modern medicine, and because of globalization, that it seems unusual.

That being said, from a theological angle, the Qur'an and hadith indicate that there are metaphysical laws for societies that go beyond material cause and effect. That is, acts of evil or injustice may bring about a negative consequence for that society even if the material chain of cause and effect is not readily apparent. (This should not be taken to mean that countries with high levels of infection currently are suffering from their own injustices; it is just a general principle.)

Our world is rife with injustice and imbalance, including warfare, sanctions, overconsumption, economic injustice, and environmental destruction. It is reasonable to look at the coronavirus situation in that light (and by "situation" I mean not only the virus but the sociopolitical response), and to consider that, in addition to material factors relating to the spread of the virus (such as airplanes and urbanization), it may be (a) an act of God designed to give us the opportunity to bring out and fix some of those problems, or (b) a natural consequence as part of metaphysical laws of cause and effect.

(Of course, all of these things often work together. In fact, even if it did transpire that it was manmade, things still happen with the permission of God; as the Qur'an says, they plan, and Allah plans, and Allah is the best of planners.)

In any case, regardless of the origins of the virus, our responses to it are manmade (even if we have little control as individuals). This includes positive responses, such as helping others, and negative responses, such as taking advantage of it for political and national gain, or hoarding. 

When individuals get sick, there is no one answer as to why - everyone's circumstances are different. One person can get sick simply as part of the natural chain of cause and effect and the spread of infection. Another can get sick as a divine test, divine trial, or to adjust their lives due to the divine decree (for instance, to stop them from moving to another country). A third person might get sick because it is their time to die, and Allah has hidden death in various causes. So, it is not possible to give one answer for what happens to individuals, although we can often get a sense of what is happening with ourselves through self-reflection. 
 

It is also a good time for prayer. Here is a prayer attributed to Imam Rida (A) in the book Tibb al-A'immah for times of plague:

In the name of Allah, the compassionate, the merciful

There is no strength or might except in Allah, the exalted, the mighty.

Nothing is of benefit without the permission of Allah. I have placed my trust in Allah. Healing can only happen through Allah. Whatever Allah wills happens, and none can dispel evil but Allah. I am sufficed by Allah who created me and therefore guides me, who grants me food and drink, and heals me when I am ill. And we have sent down from the Qur'an healing and mercy for the believers. 

O Allah, grant us well-being, and do not separate between ourselves and well-being, O creator of well-being, O most merciful of the merciful.