There exist many tick borne infections that are of either economic or public health interest. Mathematical models have previously been used to describe the dynamics of these infections. However it has recently come to light that there is an alternative mechanism for the transmission of these diseases that has not been considered in a modelling framework. This is transmission through ticks co-feeding on non-viraemic hosts. This paper extends a simple mathematical model to include this alternative transmission mechanism. The model is used to describe the dynamics of Louping ill virus in red grouse (the viraemic host) and hares (the non-viraemic host). However, these results are applicable to many other systems. The model is analysed using joint threshold density curves. It is found that the presence of a non-viraemic host allows the virus to persist more readily than it would in the presence of a host that simply amplified the tick population. More importantly, if the level of non-viraemic transmission is high enough the virus can persist in the absence of the viraemic host. This result has important implications for the control of tick borne diseases.