Effects of rising temperature and prescribed fire on Amblyomma Americanum with ehrlichiosis

Ehrlichiosis is a nationally notifiable disease in the United States and the prevalence of this disease, as with other tick-borne diseases, has been increasing since at least the year 2000. One aspect that has likely contributed to the increase in the prevalence of this disease is rising temperatures due to climate change. A promising method for control of tick populations is prescribed burning. In this study we develop a detailed mathematical model of ordinary differential equations to investigate the effect of rising temperatures on Amblyomma americanum populations in endemic and invasion scenarios. We used an impulsive system of ordinary differential equations to investigate the effects of prescribed burning on infectious ticks to determine if prescribed fire remains effective as temperatures increase under endemic and invasion scenarios. We found the following in the absence of prescribed burning: (1) as temperature increases, there are significant increases in the number of infectious questing nymphs and adults. (2) Ehrlichiosis becomes established in the questing nymph and adult tick populations quicker in an invasion scenario as temperature increases. In the presence of prescribed burning, we observed a reduction in the prevalence of infectious questing nymphs and adults. These results with prescribed burning hold regardless of increases in temperature, indicating that that prescribed burning remains an effective control method for Amblyomma americanum even in the case of a significant increase in temperature such as 2 {degrees}C and 4 {degrees}C.