"We introduced the basic reproduction ratio R0 and obtained the global dynamics of the disease in terms of R0," says Zhao. The disease is expected to die out when R0 <1 and stabilize in a positive periodic state when R0 >1. Hence, the objective is to drive R0 to less than 1. "In the case where R0 > 1, we may get an approximate value of the infection level, and then alter some parameters to drive R0 < 1 so that the disease can be eradicated ultimately," explains Zhao.
"We also established the existence and a computational formula of the spreading speed of infection when R0 > 1," says Zhao. "To control the disease, we may use strategies to reduce the spreading speed. For example, we may use some chemical methods to reduce the infection susceptibilities or the total number of hosts."
Future research involves taking into account the time between various stages of the tick life cycle. "One future direction is to incorporate time delays between tick life stages into our model," says Zhao. "Another challenging problem is to study the spreading speeds and traveling waves in the case where some parameters are spatially dependent."
|Contact: Karthika Muthukumaraswamy|
Society for Industrial and Applied Mathematics