Lyme disease imposes increasing global public health challenges. To better understand the joint effects of seasonal temperature variation and host community composition on the pathogen transmission, a stage-structured periodic model is proposed by integrating seasonal tick development and activity, multiple host species and complex pathogen transmission routes between ticks and reservoirs. Two thresholds, one for tick population dynamics and the other for
Lyme-pathogen transmission dynamics, are identified and shown to fully classify the long-term outcomes of the tick invasion and
disease persistence. Seeding with the realistic parameters, the tick reproduction threshold and
Lyme disease spread threshold are estimated to illustrate the joint effects of the climate change and host community diversity on the pattern of
Lyme disease risk. It is shown that climate warming can amplify the
disease risk and slightly change the seasonality of
disease risk. Both the "dilution effect" and "amplification effect" are observed by feeding the model with different possible alternative hosts. Therefore, the relationship between the host community biodiversity and
disease risk varies, calling for more accurate measurements on the local environment, both biotic and abiotic such as the temperature and the host community composition.