Caraco T, Gardner G, Maniatty W, Deelman E, Szymanski B K
Department of Biological Sciences, University at Albany, NY 12222, USA.
J Theor Biol. 1998 Aug 21;193(4):561-75. doi: 10.1006/jtbi.1998.0722.
Ecological interactions underlying the epidemic of Lyme disease involve a spirochete, a tick (with larval, nymph and adult stages), and two (or more) vertebrate hosts. Juvenile ticks ordinarily feed on mice; adult ticks feed on deer. Mice acquire the spirochete from infected nymphs and then pass the infection to larvae of the next tick generation. Lyme disease may result when a human is inadvertently bitten by an infectious nymph. Our model of the Lyme phenomenon counts the total number of ticks in each stage, the numbers of infected ticks by stage, and the number of infected mice. We fix the total population sizes of deer and mice, assume the ticks self-regulate, and solve the homogeneous-mixing case for equilibrium abundances. A local stability analysis identifies a condition where extinction of the spirochete is stable. Reversing this condition implies that the spirochete can invade the system of ticks and vertebrate hosts. When the spirochete can invade, a positive equilibrium number of infected organisms is locally stable. Spirochete invasion is promoted by a sufficient density of mice suffering low mortality, high susceptibility to infection in both mice and ticks, a high attack rate of ticks on mice, a high density of larval ticks, and low mortality among tick nymphs. Low mouse mortality allows the frequency of infection among nymphs to approach an individual tick's susceptibility when feeding on an infected mouse.
莱姆病流行背后的生态相互作用涉及一种螺旋体、一只蜱（有幼虫、若虫和成虫阶段）以及两个（或更多）脊椎动物宿主。幼年蜱通常以小鼠为食；成年蜱以鹿为食。小鼠从受感染的若虫那里感染螺旋体，然后将感染传递给下一代蜱的幼虫。当人类被感染的若虫意外叮咬时，可能会引发莱姆病。我们的莱姆病现象模型计算每个阶段蜱的总数、各阶段受感染蜱的数量以及受感染小鼠的数量。我们固定鹿和小鼠的总种群规模，假设蜱自我调节，并求解均匀混合情况下的平衡丰度。局部稳定性分析确定了螺旋体灭绝稳定的一种条件。逆转这种条件意味着螺旋体可以侵入蜱和脊椎动物宿主的系统。当螺旋体能够侵入时，受感染生物的正平衡数量在局部是稳定的。小鼠死亡率低、小鼠和蜱对感染的易感性高、蜱对小鼠的攻击率高、幼虫蜱密度高以及蜱若虫死亡率低，这些因素都会促进螺旋体的侵入。低小鼠死亡率使得若虫在以受感染小鼠为食时的感染频率接近单个蜱的易感性。
