Many people are hopeful that the catastrophic effects of #COVID19 would lead to the embrace of world government. Reminds me of Immanuel Kant and his ruminations on perpetual peace, and the liberals' optimistic expectation that humanity can build institutions that successfully manage the challenges of anarchy (absence of an institution akin to the state in domestic politics), and some of them who believe that these institutions can become supranational. I think Gordon Brown is following this tradition when he calls for a new global government. See: "Coronavirus: Gordon Brown calls for new global government to fight impact of Covid-19"
However, I remember that the 1970s Global South call for a New International Economic Order (NIEO) failed. See: The New New International Economic Order Calls for global governance also failed after the 2008 meltdown. Is #COVID19 the phenomenon that would catalyze the change? Unfortunately people who want world governance are underestimating the power of inertia and also status quo preference by the powerful countries and elites that currently control the global system. My take is that some reforms will happen but they will fall far short of global governance that puts in place an entity akin to the state in global politics. This is because the system is not only political, it is economic and social. The only thing that changes global systems is a system-wide war that brings another paradigm to the fore. Since the current powers that be have too much to lose from war, it probably won't be allowed. So, expect some cosmetic reforms, not fundamental change.
Also, given the US abdication of leadership of the liberal international system that it established after the second world war, China is quietly taking leadership. It is sending COVID19 help to European countries like Italy. Jack Ma of Alibaba is sending help to African and other countries. China also set up the Health Road Initiative (I may have got the name wrong). The Coronavirus Could Reshape Global Order
I know some ignorant people like him, but the Trump administration has not been up to the task of leading the international community on anything. I am not a supporter of Pax Americana, because all imperialism has warts. However, hegemony can also be used for good, like fashioning a sensible, logical and effective worldwide response to this pandemic. Trump unfortunately has squandered a great deal of the power and influence built up since the end of the second world war. The Chinese will take advantage of the power vacuum. This is the normal response of a rising power in an anarchical international system. It's what the US did after World War II and what past rising powers have done. Instead of blaming the Chinese, we should realize that China learned from the West how to maneuver and it's doing it skillfully.
The most reliable source of information on COVID19 is the World Health Organization. See: Coronavirus disease (COVID-19) Pandemic