Coutinho F A B, Burattini M N, Lopez L F, Massad E
School of Medicine, The University of São Paulo and LIM 01/HCFMUSP, Av. Dr. Arnaldo 455, São Paulo, CEP 01246-903, SP, Brazil.
Bull Math Biol. 2006 Nov;68(8):2263-82. doi: 10.1007/s11538-006-9108-6. Epub 2006 Sep 2.
A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by R, is less than 1, the disease does not invade the populations and when R is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases.
为研究登革热越冬情况，提出了一个非自治动力系统，其中对蚊媒种群的季节性变化进行了建模。推导了一个随时间变化的阈值(R(t))，使得当它的年平均值(R)小于(1)时，疾病不会侵袭种群，而当(R)大于(1)时则会侵袭。我们所说的不侵袭种群是指在随后的传播季节中，受感染个体的数量总是减少。使用相同的阈值，可以理解由此产生的疫情的所有定性特征。我们的模型表明，蚊子的经卵感染促进了登革热的越冬。我们还解释了蚊子种群高峰期与登革热病例高峰期之间的延迟。
