Basil plants (Ocimum basilicum) are particularly susceptible to aphids -- small, pear-shaped insects that feed on leaves and stems. They're not typically harmful to plants in small numbers. Whiteflies are small and yellowish in color, with white wings, and they usually cluster on the undersides of leaves. They leave behind sticky honeydew after feeding on the leaves, and can cause the leaves to turn yellow and fall off. Both types of pest are controllable, if you catch them early enough.
Handpick basil leaves off the plant and place them into a cup of soapy water if the whiteflies are in the nymph stage. You can also vacuum whiteflies from the leaves with a handheld vacuum and dispose of them. Another method is to run a stream of water over the plant to rinse away the whiteflies or aphids. Do this in the morning so the plant has time to dry out during the day. Avoid using a strong stream of water because it can tear the delicate basil leaves.
Apply a layer of reflective mulch or aluminum foil on the soil around the base of the plant. This deters aphids and whiteflies. Remove the mulch if temperatures get above 90 degrees Fahrenheit.
Spray the plant thoroughly, including the undersides of the leaves, with ready-to-use insecticidal soap or neem oil. Do this once a week until the pests are gone, and only on days when the temperature is below 90 F.