Is there any advice in the Buddhist scriptures that would help a leader balance a safe economy with people's concerns about sickness & death?

The following "advice" seems suitable for all of the people mentioned in your question. Translation and opening comment by Ven. Ṭhānissaro.

Being Consummate - Sampadā Sutta (AN 5:130)

This discourse serves as a strong reminder not to break the precepts even for the sake of people or things one holds dear.

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“Monks, there are these five kinds of loss. Which five? Loss of relatives, loss of wealth, loss through disease, loss in terms of virtue, loss in terms of views. It’s not by reason of loss of relatives, loss of wealth, or loss through disease that beings—with the break-up of the body, after death—reappear in a plane of deprivation, a bad destination, a lower realm, hell. It’s by reason of loss in terms of virtue and loss in terms of views that beings—with the break-up of the body, after death—reappear in a plane of deprivation, a bad destination, a lower realm, hell. These are the five kinds of loss.

“There are these five ways of being consummate. Which five? Being consummate in terms of relatives, being consummate in terms of wealth, being consummate in terms of freedom from disease, being consummate in terms of virtue, being consummate in terms of views. It’s not by reason of being consummate in terms of relatives, being consummate in terms of wealth, or being consummate in terms of freedom from disease that beings—with the break-up of the body, after death—reappear in a good destination, a heavenly world. It’s by reason of being consummate in virtue and being consummate in terms of views that beings—with the break-up of the body, after death—reappear in a good destination, a heavenly world. These are the five ways of being consummate.”

What do you think, great king? Suppose a man, trustworthy and reliable, were to come to you from the east and on arrival would say: 'If it please your majesty, you should know that I come from the east. There I saw a great mountain, as high as the clouds, coming this way, crushing all living beings [in its path]. Do whatever you think should be done.' Then a second man were to come to you from the west... Then a third man were to come to you from the north... Then a fourth man were to come to you from the south and on arrival would say: 'If it please your majesty, you should know that I come from the south. There I saw a great mountain, as high as the clouds, coming this way, crushing all living beings. Do whatever you think should be done.' If, great king, such a great peril should arise, such a terrible destruction of human life — the human state being so hard to obtain — what should be done?"

"If, lord, such a great peril should arise, such a terrible destruction of human life — the human state being so hard to obtain — what else should be done but Dhamma-conduct, right conduct, skillful deeds, meritorious deeds?"

SN 3.25

1. The government and leaders should provide just protection and security to its citizens. Basically, they should undertake the right measures to take care of their people.

From DN 26:

‘But sire, what are the noble duties of a wheel-turning monarch?’

‘Well then, my dear, relying only on principle—honoring, respecting, and venerating principle, having principle as your flag, banner, and authority — provide just protection and security for your court, troops, aristocrats, vassals, brahmins and householders, people of town and country, ascetics and brahmins, beasts and birds. Do not let injustice prevail in the realm. Pay money to the penniless in the realm.

2. The lay Buddhist should play the role of a good patient and heed the advice of competent authorities.

From Kucchivikara-vatthu of the Vinaya, the Buddha taught:

"A sick person endowed with five qualities is easy to tend to: he does what is amenable to his cure; he knows the proper amount in things amenable to his cure; he takes his medicine; he tells his symptoms, as they actually are present, to the nurse desiring his welfare, saying that they are worse when they are worse, improving when they are improving, or remaining the same when they are remaining the same; and he is the type who can endure bodily feelings that are painful, fierce, sharp, wracking, repellent, disagreeable, life-threatening. A sick person endowed with these five qualities is easy to tend to.

3. Buddhist leaders should set a good example as the Dalai Lama had done (from this article).

The exiled Tibetan spiritual leader His Holiness the Dalai Lama has received his second dose of the Covishield vaccine at his residence on Monday, according to CTA run Tibet.net. He received the first jab on March 6 at Zonal hospital in Dharamshala.

“The vaccine was administered by a medical team of Delek hospital led by Dr Tseten Dorjee, personal physician to His Holiness,” Tibet.net reported. The entire staff and security details of His Holiness, including those living in the residence, were also vaccinated, the report further stated. ...

The Nobel laureate wrote that he has been following the alarming news of the pandemic across the world, especially including in India. “May I take this opportunity to express my deep appreciation for all the efforts that are being made to tackle this devastating pandemic, especially by those courageously working on the frontline. I pray that the pandemic threat will end soon,” he wrote. ...

The Dalai Lama cancelled all his public engagements since February last year and engaged with the pubic through virtual platform for teachings and other interactive dialogues with students, Buddhist followers, and various organizations from all across the world. The Buddhist leader’s only public appearance since the lockdown was during his first Covishied jab at the local hospital last month, where he urged others to take the injection, “I want to share that more people should have the courage to take this injection.”