按年龄、感染时间和免疫力下降构建的人媒疟疾传播模型
Human-vector malaria transmission model structured by age, time since infection and waning immunity
摘要：
与关于人-蚊子疟疾感染的传播的许多理论研究相反，很少有研究考虑多结构模型公式，包括（i）人和蚊子种群的实足年龄，（ii）自从人和蚊子被感染以来的时间和（iii）人免疫力减弱（即，恢复后保护性抗体的逐渐丧失）。这些结构变量被充分证明是人-蚊子疟疾感染传播的基础。在这里，我们制定了一个年龄结构模型占三个结构变量。利用积分半群理论，我们首先处理所提出的模型的适定性。我们还研究了模型平衡态的存在性。无病平衡点总是存在的，而地方病平衡点的存在性进行了讨论。我们推导出阈值R 0（基本再生数）。这里获得的R 0的表达特别突出了上述结构变量对人-病媒关联的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。其次，我们得到了一个地方病平衡点分支的充要条件。在一些配置中，人口的年龄结构被忽略，我们表明，根据一些常数Cbif的参数给出的符号，分叉发生在R 0 = 1，这是向前或向后。在前一种情况下，它意味着存在（唯一）地方病平衡点当且仅当R 0> 1。在后一种情况下，当R 0 << 1足够小时不存在地方病平衡点，当R 0> 1时存在唯一性，而当0 <<R 0 < 1足够接近1时存在多个地方病平衡点。
英文摘要：
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). 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
