A discrete stochastic model of the transmission cycle of the tick borne encephalitis virus

Tick borne encephalitis (TBE) is an emergent zoonosis transmitted by ticks in several woodland areas of the Eurasia. The ethiological agent is a Flavivirus causing in men severe consequences - such as meningoencephalitis - in some cases leading to death. TBE is naturally maintained by a cycle involving hard ticks belonging to the Ixodes spp. as vectors and mice as hosts animals. In fact, hard ticks need only one complete blood meal to moult. Furthermore, immature ticks - larvae and nymphs - usually feed on small vertebrates while adults ticks prefers large mammals. However, the main route of transmission of the TBE viruses arises from infected nymphs to larvae cofeeding on the same mice. In this work we try to formulate a discrete stochastic model that describes the aforementioned transmission cycle. In particular, we consider a stochastic network contact structure in order to describe the potential numbers of transmissions from nymphs to larvae over different months in years. From this mathematical model we have achieved some interesting analytical results that in the future we intend to validate by stochastic simulations.