Can rabies virus survive outside host on grass or leaves under sunlight?

First things first: Rabies is an extremely dangerous infection and regular vaccination (every 10 years) is the only sure protection! As far as I know there are about 15 - 20 people who have ever survived an acute rabies infection in the history of human medicine, none of them without severe neurological sequelae and most of them died a few months after. The first reported case of a survival was Jeanna Giese in 2004.

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Now to your question:

Technically viruses are not alive in the biological sense, so medical scientists speak of viruses being active (alive, infectious) or inactive (dead, destroyed, unable to infect a cell).

Yes the rabies virus can stay active outside of a host body for a limited time, depending on environmental factors.

This german veterinary gives the following information:

• The virus occurs in the body fluids like saliva, blood, urine and milk of infected animals. To infect a new host, a certain number of viruses has to be transmitted and infections seem only possible by direct contact of infected saliva to mucosa or fresh wounds.
• Indirect contact (an infected animal leaves saliva on an object which is then touched by a healthy human) is very unlikely but not excluded to cause infections.
• The virus becomes inactive within one day in dry conditions and under UV light (natural sunlight).
• It can be inactivated by temperatures above 50°C / 122°F in a few minutes of time
• It can stay active and infectious for several days in a dark, humid environment around 23°C / 73°F.

In addition, the safety data sheet of MSDS Online contains the following information about the virus:

• Rabies virus is inactivated by exposure to 70% ethanol, phenol, formalin, ether, trypsin, β-propiolactone, and some other detergents
• Rabies virus does not tolerate pH below 3 or above 11, and is inactivated by ultraviolet light.
• This virus does not survive well outside its host (in dried blood and secretions) as it is susceptible to sunlight and desiccation.

And from this scientific study (Matouch et al, Vet Med (Praha) 1987), which was summarized here, comes the longest recorded activity time of the virus outside of a host:

• When the virus was spread in a thin layer onto surfaces like glass, metal or leaves, the longest survival was 144 hours at 5 °C / 41°F (that's 6 full days!)
• At 20°C / 68°F, the virus was infective for 24h on glass and leaves and 48h on metal.
• At 30°C / 86°F, the virus was inactivated within 1.5h with exposure to sunlight and 20h without sunlight.