Keywords
ixodes scapularis, mathematical modelling, temperature, lyme disease, dynamics
Start Date
1-7-2010 12:00 AM
Abstract
Lyme disease has been recognised as one of the emerging vector borne diseases in Canada. Ticks, Ixodes scapularis SAY, play a major role as vectors of Lyme disease causative agent Borrelia burgdorferi. Ticks become infected with Borrelia while feeding on the primary hosts (mice, squirrels, shrews, and other small vertebrates). Deers are primary source of nourishment for each gravid female I. scapularis and are fundamental to the tick establishment without infection. The life cycle of tick, I. scapularis, is very complex and takes nearly two years to reach adult stage from egg. Studies have shown that tick life cycle is heavily influenced by changes in the climate. In particular, increasing temperature was shown to facilitate the rapid geographical expansion of vector I. scapularis and such an expansion might establish the disease in non-endemic areas of Canada. Hence, we tried to predict the temperature impact on the complex tick population life cycle as well as on their establishment conditions in the presence of primary and secondary hosts. This tick population model was based on the Ogden’s process-based system, which comprises 12 mutually exclusive tick stages. Tick developmental rates were modelled as temperature dependent based on the earlier studies. We found the threshold condition, in terms of the basic reproduction number (R0), for tick persistence and showed the existence, uniqueness and stability of an endemic equilibrium. We also conducted some numerical simulations to illustrate the analytical results. These simulation results seem to be in good agreement with the previous studies on Lyme disease ecology, and our analysis indicates that temperature can be used as determining parameter to predict the distribution, establishment of tick populations and Lyme disease in the new regions.
Modeling dynamical temperature influence on tick Ixodes scapularis population
Lyme disease has been recognised as one of the emerging vector borne diseases in Canada. Ticks, Ixodes scapularis SAY, play a major role as vectors of Lyme disease causative agent Borrelia burgdorferi. Ticks become infected with Borrelia while feeding on the primary hosts (mice, squirrels, shrews, and other small vertebrates). Deers are primary source of nourishment for each gravid female I. scapularis and are fundamental to the tick establishment without infection. The life cycle of tick, I. scapularis, is very complex and takes nearly two years to reach adult stage from egg. Studies have shown that tick life cycle is heavily influenced by changes in the climate. In particular, increasing temperature was shown to facilitate the rapid geographical expansion of vector I. scapularis and such an expansion might establish the disease in non-endemic areas of Canada. Hence, we tried to predict the temperature impact on the complex tick population life cycle as well as on their establishment conditions in the presence of primary and secondary hosts. This tick population model was based on the Ogden’s process-based system, which comprises 12 mutually exclusive tick stages. Tick developmental rates were modelled as temperature dependent based on the earlier studies. We found the threshold condition, in terms of the basic reproduction number (R0), for tick persistence and showed the existence, uniqueness and stability of an endemic equilibrium. We also conducted some numerical simulations to illustrate the analytical results. These simulation results seem to be in good agreement with the previous studies on Lyme disease ecology, and our analysis indicates that temperature can be used as determining parameter to predict the distribution, establishment of tick populations and Lyme disease in the new regions.
