Modeling the differential effect of prescribed fire on multi-vector tick-borne tularemia disease

Tularemia is a zoonotic disease caused by Francisella tularensis bacteria, a gram-negative coccobacillus-shaped bacterium. There are multiple transmission routes of the infection to humans such as consumption of contaminated food or water, handling of infected animals or bites from haematophagous arthropods (such as ticks, deer flies, or mosquitoes). In this study, we focus on transmission via the bites of ticks and developed a deterministic model of ordinary and impulsive differential equations to gain insight about the differential effect of prescribed fire on Dermacentor variabilis and Amblyomma americanum ticks and the prevalence of tularemina. We found that prescribed fire differentially reduce the number of the two ticks with A. americanum reduced the least compare to D. variabilis subsequently leading to differential increase of tularemia new infected cases in humans and rodents. Our result further indicates that the spatial arrangement of burn against unburn areas may not matter for humans and D. variabilis unlike A. americanum and the rodents which had more infected in unburn areas compare to burn areas when prescribed fire was implemented. The results of this study provide important new understandings of the intricate effect of prescribed fire on tick species, and the dynamics of the tick-borne disease.