Abstract：
BACKGROUND: Malaria is the world\'s most fatal and challenging parasitic disease, caused by the Plasmodium parasite, which is transmitted to humans by the bites of infected female mosquitoes. Bangladesh is the most vulnerable region to spread malaria because of its geographic position. In this paper, we have considered the dynamics of vector-host models and observed the stochastic behavior. This study elaborates on the seasonal variability and calculates the probability of disease outbreaks.
METHODS: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation.
RESULTS: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or vector. Additionally, periodic transmission rates have a great influence on the probability outbreak. The basic reproduction number (R0) is derived, which is the main justification for studying the dynamical behavior of epidemic models.
CONCLUSIONS: Seasonal variability significantly impacts malaria transmission, and the probability of disease outbreaks is influenced by time and the initial number of infected individuals. Moreover, the branching process approximation is applicable when the population size is large enough and the basic reproduction number is less than 1. In the future, such analysis can help decision-makers understand the impact of various parameters and their stochastic behavior in the vector-host model to prevent such types of disease outbreaks.
METHODS: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation.
RESULTS: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or vector. Additionally, periodic transmission rates have a great influence on the probability outbreak. The basic reproduction number (R0) is derived, which is the main justification for studying the dynamical behavior of epidemic models.
CONCLUSIONS: Seasonal variability significantly impacts malaria transmission, and the probability of disease outbreaks is influenced by time and the initial number of infected individuals. Moreover, the branching process approximation is applicable when the population size is large enough and the basic reproduction number is less than 1. In the future, such analysis can help decision-makers understand the impact of various parameters and their stochastic behavior in the vector-host model to prevent such types of disease outbreaks.
摘要：
背景：疟疾是世界上最致命和最具挑战性的寄生虫病，由疟原虫寄生虫引起的，通过受感染的雌性蚊子的叮咬传播给人类。由于其地理位置，孟加拉国是最容易传播疟疾的地区。在本文中,我们考虑了向量-宿主模型的动力学，并观察了随机行为。本研究详细阐述了季节性变化，并计算了疾病爆发的概率。
方法：我们提出了疟疾疾病传播模型，并开发了其相应的连续时间马尔可夫链（CTMC）表示。提出的矢量宿主模型说明了疟疾传播模型以及敏感性分析。描述了具有CTMC曲线的确定性模型，以显示真实场景中的随机性。按顺序,我们将这些研究扩展到包含季节性变化的时变随机向量-宿主模型。进行相平面分析以探索该疾病的特征，检查各个隔室之间的相互作用，并评估关键参数的影响。为相应的向量-宿主模型开发了分支过程近似，以计算爆发概率。为了观察分析研究，完成了许多数值结果。
结果：季节性和接触模式影响疾病爆发的动态。数值说明提供了疾病爆发的概率取决于受感染的宿主或媒介。此外,周期性传播率对爆发概率有很大影响。导出基本再现数(R0)，这是研究传染病模型动力学行为的主要依据。
结论：季节变化显著影响疟疾传播，疾病爆发的可能性受时间和初始感染个体数量的影响。此外，当种群规模足够大且基本繁殖数小于1时，分支过程近似适用。在未来,这种分析可以帮助决策者了解各种参数的影响及其在载体-宿主模型中的随机行为，以防止此类疾病爆发。
方法：我们提出了疟疾疾病传播模型，并开发了其相应的连续时间马尔可夫链（CTMC）表示。提出的矢量宿主模型说明了疟疾传播模型以及敏感性分析。描述了具有CTMC曲线的确定性模型，以显示真实场景中的随机性。按顺序,我们将这些研究扩展到包含季节性变化的时变随机向量-宿主模型。进行相平面分析以探索该疾病的特征，检查各个隔室之间的相互作用，并评估关键参数的影响。为相应的向量-宿主模型开发了分支过程近似，以计算爆发概率。为了观察分析研究，完成了许多数值结果。
结果：季节性和接触模式影响疾病爆发的动态。数值说明提供了疾病爆发的概率取决于受感染的宿主或媒介。此外,周期性传播率对爆发概率有很大影响。导出基本再现数(R0)，这是研究传染病模型动力学行为的主要依据。
结论：季节变化显著影响疟疾传播，疾病爆发的可能性受时间和初始感染个体数量的影响。此外，当种群规模足够大且基本繁殖数小于1时，分支过程近似适用。在未来,这种分析可以帮助决策者了解各种参数的影响及其在载体-宿主模型中的随机行为，以防止此类疾病爆发。
