As a leader, you are in a tough situation right now: vital decisions must be made quickly. How do you keep the business running, minimizing the economic impacts? How do you reduce the risk of infection for employees and customers? How do you communicate effectively with all internal and external stakeholders without neglecting other obligations?
German Chancellor Angela Merkel said yesterday that we are facing the biggest challenge since World War II, and that does not seem exaggerated. 
However, leaders are human beings too, and you, like anybody else, may experience fear, anxiety, and worries. It is normal and has nothing today with weakness. In fact, it would be quite unusual if the current situation did not impact you emotionally at all.
Let us have a brief look at how the brain works:
One key insight from neuroscience of the recent decades is that we are not rational beings. We are rationalizing. I.e., we are primarily driven by our emotions, and then we make sense of what we experienced only later 
Fear is one of the strongest emotions we can experience. It is not a negative emotion; in fact, fear is very useful, and we would not be where we are today if we had not developed very effective fear-responses over millions of years of evolution.
Our brain allocates energy to where it is needed the most in any given moment. During our hunter-gatherer times, it was vital to notice the tiger in the bushes behind us  and react to such threats instantly. Within milliseconds, fear would prepare your body for freeze, fight, or flight. Eventually, your brain would allocate all available energy to running as fast as possible. You would not think about food or sex. All you would do would be literally running for your life.
Today, our brains are basically still the same as those of our hunter-gatherer ancestors. We may rarely encounter threats from wild tigers these days, but the same old fight, flight, or freeze response of the brain kicks in the moment we perceive a threat, no matter how “real” this threat might be or not.
When your brain has identified a potential danger, your body will go into survival mode. Energy is allocated to where it is needed most, and that is protecting yourself. Consequently, this energy is not available to creative thinking as it would be under normal circumstances.
COVID-19 is a threat. While the chances of a fatal infection are apparently relatively low for an individual, there are numerous other risks: you could carry the virus without showing any symptoms, and you could infect other people who might then suffer from a more severe, eventually deadly infection. There seems no doubt that the economic downturn will continue for a while, and many businesses will not survive. This is a real threat, too. Uncertainty triggered by more and more bad news by the hour certainly stokes fears.
Intellectually, you know that constant worrying does not help, but since human beings are driven by emotions, rational insight cannot prevent fear and anxiety from taking over and become overpowering for some.
The intensity of the fear response is different for each individual. Just like some people are easily overwhelmed in a stressful situation, others will strive under the same conditions.
What I am trying to say here is: if you are a leader who is less emotionally affected by the crisis, others will appreciate your empathy with those who struggle more than you. But even if you are a very seasoned leader, you are still a human being, and you may encounter fear and anxiety just like anybody else. Remember, this is not weakness, this is human.
It is human to acknowledge that right now, you might be confronted with the biggest challenge in your career ever. Fear triggers your brain to allocate energy for survival, and so you need to acknowledge that you and the people you work with cannot perform as usual. I certainly realize that I am not at my best these days, and I hear the same from everyone I talk to. 
A problem is that our body has evolved to deal with short-term high-intensity stress (the tiger in the bushes), but not for the longterm low-level stress most of us are experiencing these days: amongst others, cortisol levels in your body rise, leading to less and lower quality of sleep. And less and worse sleep for a prolonged time weakens your immune system. You are trapped in a vicious cycle.
Most of us will encounter a critical situation for an extended period of time. So, what can you do?
First of all, have compassion for others but also for yourself. Make sure that you give self-care high priority. Getting enough sleep, healthy nutrition, and regular exercise are critical.
For your mental well-being, meditation may be the method of choice. An efficient exercise for these days can be to notice that, probably, you are ok right now. 
Practice physical distancing, not social distancing. Another crucial insight from neuroscience is that we are social beings and that relationships are more important for humans than most might think.  While the virus spreads from human to human, reducing physical contact with others appears to be the best way to keep the pandemic in check. But physical distancing does not mean not having any social contacts anymore. On the contrary: staying connected with others is critical for your well-being. 
So, keep talking to people (maybe use video conferencing or the good old phone instead of face-to-face contact), listen to their problems, and make sure you have someone to listen to you. No matter how high you are in the corporate hierarchy, you are still human, and as explained, fear and anxiety are perfectly normal reactions to the current crisis. I know from experience that it can be quite lonely at the top; whether you are the CEO or a department head, we all need support.
May you be well!
 https://www.bundesregierung.de/breg-de/themen/coronavirus/ansprache-der-kanzlerin-1732108, last accessed on March 19, 2020
 Emotions take place in the brain about three times faster than cognition. For a detailed explanation in the context of leadership, I recommend Paul Brown, Joan Kingsley, Sue Paterson: The Fear-free Organization: Vital Insights from Neuroscience to Transform Your Business Culture, 2015, Kogan Page
 Cf., Rick Hanson, Buddha’s Brain: The Practical Neuroscience of Happiness, Love, and Wisdom, New Harbinger Publications, 2009
 A friend of mine is an experienced psychologist and coach, and he just told me yesterday that he sees depression on the rise as a result of this crisis.
 see e.g., Rick Hanson “Notice You’re Alright Right Now” https://www.rickhanson.net/notice-youre-alright-right-now/ and his other guided meditations such as https://www.rickhanson.net/growing-the-good-monthly-live-meditation-program/, links last accessed on March 19, 2020
 In the 1940ies, Austrian psychologist René Spitz found that love and care are critical for survival. He compared children in an orphanage, cared for by professional nurses, with children who grew up in prison, cared for by their imprisoned mothers. Although the physical conditions in the orphanage were better, the death rates were significantly higher than for the children in the prison: within two years, 37% of the orphans died, whereas all the prison children were still alive after five years. (cf., René Árpád Spitz; Hospitalism, in R. S. Eissler, (Ed.) The psychoanalytic study of the child (Vol. I). New York: International Universities Press, 1945, or René Árpád Spitz: Hospitalism: A follow-up report in R. S. Eissler, (Ed.) The psychoanalytic study of the child (Vol. II). New York: International Universities Press, 1946). Also, in our modern lives today, studies indicate that “People who are more socially connected to family, friends, and community are happier, healthier, and live longer than people who are less well connected.” (Harvard Health Letter: Can relationships boost longevity and well-being?, June 2017, https://www.health.harvard.edu/mental-health/can-relationships-boost-longevity-and-well-being last accessed on March 19, 2020) In contrast, loneliness leads to less happiness, earlier health decline, and decline of brain function.
 Have you ever wondered why solitary confinement is considered the worst punishment in prisons? Cf. https://en.wikipedia.org/wiki/Solitary_confinement, last accessed on March 19, 2020