Kotola Belela Samuel, Teklu Shewafera Wondimagegnhu
Department of Mathematics, Oda Bultum University, Chiro, Ethiopia.
Department of Mathematics, Natural and Computational Sciences, Debre Berhan University, Ethiopia.
Heliyon. 2024 May 22;10(11):e31760. doi: 10.1016/j.heliyon.2024.e31760. eCollection 2024 Jun 15.
Because of its high contagiousness and correlation with HIV/AIDS complaints, the virus that causes varicella-zoster virus and its interactions have major consequences for a considerable portion of people worldwide. The primary aim of this work is to suggest and examine optimal control methods for managing the transmission dynamics of HIV/AIDS and Varicella-Zoster co-infection, using an integer model approach. The mathematical analyses of the proposed integer order model places particular emphases on the boundedness and non-negativity of the model solutions, scrutinizing equilibrium points, determining the models basic reproduction ratios (the models basic reproduction numbers) through the next-generation matrix operator method, and assessing the model equilibrium points existences and stabilities in local approach by considering the local stability conditions of Routh and Hurwitz. Additionally, it incorporates an optimal control framework to enhance our understanding of the dynamics involved in the spreading of HIV/AIDS and Varicella-Zoster co-infection within a considered population. This entails determining preventative measures that can be deliberately put into place to lessen the effects of these co-infections. The solutions of the HIV/AIDS and Varicella-Zoster co-infection model converges to the co-infection endemic equilibrium point whenever the associated basic reproduction number is greater than unity, as verified by numerical simulation results. Including optimal management gives the research an innovative viewpoint and helps identify tactical ways to mitigate the negative effects of this co-infection on the public health. The results highlight how crucial it is to address these complex structures in order to protect and improve public health outcomes. Implementing the proposed protection measures and treatment measures simultaneously has most effective result to minimize and eliminate the HIV/AIDS and Varicella-Zoster co-infection disease throughout the population.
由于水痘带状疱疹病毒具有高度传染性且与艾滋病相关症状有关，该病毒及其相互作用对全球相当一部分人产生了重大影响。这项工作的主要目的是使用整数模型方法，提出并检验管理艾滋病毒/艾滋病与水痘带状疱疹合并感染传播动态的最优控制方法。对所提出的整数阶模型进行数学分析时，特别强调模型解的有界性和非负性，仔细研究平衡点，通过下一代矩阵算子方法确定模型的基本再生数，并根据劳斯和赫尔维茨的局部稳定性条件，在局部方法中评估模型平衡点的存在性和稳定性。此外，它还纳入了一个最优控制框架，以加深我们对艾滋病毒/艾滋病与水痘带状疱疹合并感染在特定人群中传播所涉及动态的理解。这需要确定可以有意采取的预防措施，以减轻这些合并感染的影响。数值模拟结果验证了，只要相关的基本再生数大于1，艾滋病毒/艾滋病与水痘带状疱疹合并感染模型的解就会收敛到合并感染的地方病平衡点。纳入最优管理为该研究提供了一个创新视角，并有助于确定减轻这种合并感染对公共卫生负面影响的策略性方法。结果凸显了应对这些复杂结构对于保护和改善公共卫生结果的至关重要性。同时实施所提出的保护措施和治疗措施，对于在整个人口中最小化和消除艾滋病毒/艾滋病与水痘带状疱疹合并感染疾病具有最有效的效果。
