社区无知对登革热种群动态影响的数学分析

IF 1.3 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Frontiers in Applied Mathematics and Statistics Pub Date : 2023-04-26 DOI:10.3389/fams.2023.1094971
D. Aldila, Chita Aulia Puspadani, Rahmi Rusin
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引用次数: 1

摘要

这项研究提出了一个登革热传播模型,该模型考虑了非线性传播率,以解决人类在其环境中对登革热的无知程度。已经提出了SIR−UV模型,其中SIR表示人类种群的分类,UV表示蚊子种群的分类。假设总人口是恒定的,蚊子种群已经处于稳态条件下,使用准稳态近似(QSSA)方法,我们将SIR−UV模型简化为更简单的IR模型。我们的分析结果表明,当基本繁殖数<1时,存在稳定的无病平衡。此外,我们的模型还显示了后向分叉的可能性。社会对登革热越是无知,出现后向分叉现象的可能性就越高。因此,基本繁殖数<1的条件不足以保证登革热在种群中的灭绝。此外,我们发现,提高恢复率、降低免疫力下降率和蚊子的预期寿命可以降低后向分叉现象的可能性。我们使用雅加达的登革热发病率数据来校准我们模型中的参数。通过快速傅立叶变换分析发现,雅加达登革热发病具有52.4、73.4和146.8周的周期性。这一结果表明,登革热至少每年都会在雅加达周期性出现。通过确定三个最主要的频率,将人类的感染率假设为正弦函数,对我们的模型参数进行参数估计。进行了数值和敏感性分析,以观察社区无知对登革热流行性的影响。从敏感性分析中,我们发现,尽管更大的社区无知会引发后向分叉,但可以通过提高恢复率、延长时间免疫力或减少蚊子数量来最小化这一阈值。因此,为了更有效地控制登革热的传播,政府为减少社区的无知而开展的媒体宣传活动应辅以其他干预措施,如在医院接受良好治疗或病媒控制计划。有了这种干预措施的结合,当基本繁殖数量小于1时,将更容易达到无登革热人群的状态。
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Mathematical analysis of the impact of community ignorance on the population dynamics of dengue
This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.
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来源期刊
Frontiers in Applied Mathematics and Statistics
Frontiers in Applied Mathematics and Statistics Mathematics-Statistics and Probability
CiteScore
1.90
自引率
7.10%
发文量
117
审稿时长
14 weeks
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