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Disease caused by whitefly-transmitted begomoviruses are problematic in many tropical and subtropical world regions and cause heavy losses in food and fiber crops grown there. The whitefly, Bemisia tabaci, shows a lifecycle that includes eggs, nymphs and adults. It has several biotypes, but the B biotype is responsible for spreading plant diseases, since it has many plants species as natural hosts including weeds.

The begomoviruses includes the Tomato Severe Rugose Virus (TSRV), which is manifested in the infected plant as yellow mosaic or mottling, leaf distortion and crinkling and stunting.

The transmission occurs after the whitefly reach the phloem of an infected plant and then reach the phloem of a healthy plant. To control the disease, it is recommended to keep a plant-free period, in order to diminish the whitefly population.

Develop a mathematical model combining epidemiological and ecological dynamics that describes the interaction between whiteflies, tomatoes and the disease. Use it to understand the ecological and epidemiological consequences of the disease dynamics of TSRV.

Model the dynamic of the whitefly using three lifecycle stages: egg, nymph and adult. Combine it with the disease dynamics of TSRV. Note that, there are latency period after the whitefly and after the plant having acquired the virus, but for a first analysis it can be neglected. Answer the questions:

• Is it really necessary to clear fields before new plantings (to eliminate reservoir of disease)?
• Or is it better to increase the time between plantings?
• This whitefly species is also a disease vector for other plants, like potatoes, how can your model give us hint on other agricultural problems like this?

Barbosa, J.C., Rezende, J.A. and Amorim, L., 2016. Temporal dynamics of Tomato severe rugose virus and Bemisia tabaci in tomato fields in São Paulo, Brazil. Journal of Phytopathology, 164(1), pp.1-10.