Modeling the effects of Ehrlichia Chaffeensis and movement on dogs

Ehrlichia chaffeensis is a tick-borne infectious disease transmitted by amblyomma americanum tick. This infectious disease was discovered in the 1970s when military dogs were returning from the Vietnam war. The disease was found to be extremely severe in German Shepards, Doberman Pinschers, Belgium Malinois, and Siberian Huskies. In this study, we developed a mathematical model for dogs and ticks infected with ehrlichia chaffeensis with the aim of understanding the impact of movement on dogs as they move from one location to another. This could be a dog taken on a walk in an urban area or on a hike in the mountains. We carried out a global sensitivity analysis with and without movement between three locations using as response functions the sum of acutely and chronically infected and the sum of infected ticks in all life stages. The parameters with the most significant impact on the response functions are dogs disease progression rate, dogs chronic infection progression rate, dogs recovery rate, dogs natural death rate, acutely and chronically infected dogs disease induced death rate, dogs birth rate, eggs maturation rates, tick biting rate, dogs and ticks transmission probabilities, ticks death rate, and the location carrying capacity. Our simulation results show that infection in dogs and ticks are localized in the absence of movement and spreads between locations with highest infection in locations with the highest rate movement. Also, the effect of the control measures which reduces infection trickles to other locations (trickling effect) when control are implemented in a single location. The trickling effect is strongest when control is implemented in a location with the highest movement rate into it.