论文标题
人类媒介疟疾传播模型是按年龄结构的，自感染和免疫力减弱的时间
Human-vector malaria transmission model structured by age, time since infection and waning immunity
论文作者
论文摘要
In contrast to the many theoretical studies on the transmission of human-mosquitoes malaria infection, few studies have considered a multiple structure model formulations including (i) the chronological age of humans and mosquitoes population, (ii) the time since humans and mosquitoes are infected and (iii) humans waning immunity (i.e., the progressive loss of protective antibodies after recovery).这种结构变量已充分记录在人类疟疾感染的传播基础上。在这里，我们为三个结构变量制定了年龄结构化模型。使用综合的半群理论，我们首先处理所提出的模型的适当性。我们还研究了模型稳态的存在。在讨论了流行均衡的情况下，总是存在无疾病的平衡。我们得出阈值R0（基本复制号）。这里获得的R0的表达特别强调了上述结构变量对人类媒介关联关键重要流行病学特征的影响。这包括人类和蚊子的传播概率和存活率。接下来，我们得出了一种必要且充分的条件，暗示了地方性平衡的分叉。在某些配置中，在忽略了人口的年龄结构的某些配置中，我们表明，根据参数给出的某些恒定CBIF的迹象，在R0 = 1处发生分叉，向前或向后发生。在前一种情况下，这意味着在且仅当R0> 1时存在一个（唯一的）地方性平衡。在后一种情况下，R0 << 1足够小的r0 << 1，如果R0> 1的存在，则在0 << r0 <1足够接近1时存在唯一的平衡。
In contrast to the many theoretical studies on the transmission of human-mosquitoes malaria infection, few studies have considered a multiple structure model formulations including (i) the chronological age of humans and mosquitoes population, (ii) the time since humans and mosquitoes are infected and (iii) humans waning immunity (i.e., the progressive loss of protective antibodies after recovery). Such structural variables are well documented to be fundamental for the transmission of human-mosquitoes malaria infections. Here we formulate an age-structured model accounting for the three structural variables. Using integrated semigroups theory, we first handle the well-posedness of the model proposed. We also investigate the existence of model's steady-states. A disease-free equilibrium always exists while the existence of endemic equilibria is discussed. We derive the threshold R0 (the basic reproduction number). The expression of the R0 obtained here particularly highlight the effect of above structural variables on key important epidemiological traits of the human-vector association. This includes, humans and mosquitoes transmission probability and survival rates. Next, we derive a necessary and sufficient condition that implies the bifurcation of an endemic equilibrium. In some configuration where the age-structure of the human population is neglected, we show that, depending on the sign of some constant Cbif given by the parameters, a bifurcation occurs at R0 = 1 that is either forward or backward. In the former case, it means that there exists a (unique) endemic equilibrium if and only if R0 > 1. In the latter case, no endemic equilibrium exists for R0<< 1 small enough, a unique exists if R0 > 1 while multiple endemic equilibria exist when 0 <<R0 < 1 close enough to 1.
