Abstract

Dengue fever is a common disease which can cause shock, internal bleeding, and death in patients if a second infection is involved. In this paper, a multi-serotype dengue model with nonlinear incidence rate is formulated to study the transmission of two dengue serotypes. The dynamical behaviors of the proposed model depend on the threshold value \(R_{{0}}^{{n}}\) known as the reproductive number which depends on the associated reproductive numbers with serotype-1 and serotype-2. The value of \(R_{{0}}^{{n}}\) is used to reflect whether the disease dies out or becomes endemic. It is found that the proposed model has a globally stable disease-free equilibrium if \(R_{{0}}^{{n}}\leq 1\), which indicates that if public health measures that make (and keep) the threshold to a value less than unity are carried out, the strategy in disease control is effective in the sense that the number of infected human and mosquito populations in the community will be brought to zero irrespective of the initial sizes of sub-populations. When \(R_{{0}}^{{n}}>1\), the endemic equilibria called the co-existence primary and secondary infection equilibria are locally asymptotically stable. The effects of cross immunity and nonlinear incidence rate are explored using data from Thailand to determine the effective strategy in controlling and preventing dengue transmission and reinfection.

中文翻译：

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交叉免疫和非线性发病率对两种登革热血清型传播动力学作用的数学评估

摘要

登革热是一种常见疾病，如果涉及第二次感染，会导致休克，内部出血和死亡。本文建立了具有非线性发病率的多血清型登革热模型，以研究两种登革热血清型的传播。所提出模型的动力学行为取决于称为生殖数的阈值\（R _ {{0}} ^ {{n}} \），该阈值取决于与血清型1和血清型2相关的生殖数。的值\（R _ {{0}} ^ {{N}} \）是用来反映疾病是否死亡出或变得流行。发现如果\（R _ {{0}} ^ {{n}} \ leq 1 \），建议的模型具有全局稳定的无病平衡。，这表明如果执行使（并保持）阈值小于1的公共卫生措施，则疾病控制策略在某种意义上是有效的，因为社区中被感染的人类和蚊子数量将达到不论子群体的初始大小如何，均应归零。当\（R _ {{0}} ^ {{n}}> 1 \）时，称为同时存在的主要和次要感染均衡的地方性均衡在局部渐近稳定。利用泰国的数据探索了交叉免疫和非线性发病率的影响，以确定控制和预防登革热传播和再感染的有效策略。