Acay Bahar, Inc Mustafa, Khan Amir, Yusuf Abdullahi
Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey.
Department of Medical Research, China Medical University, Taichung, Taiwan.
J Appl Math Comput. 2021;67(1-2):755-783. doi: 10.1007/s12190-021-01502-3. Epub 2021 Feb 12.
This study provides a detailed exposition of in-hospital community-acquired methicillin-resistant (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative. We show the existence and uniqueness of the solutions of the fractional staph infection model through fixed-point theorems. Moreover, stability analysis and iterative solutions are furnished by the recursive procedure. We make use of the parameter values obtained from the Beth Israel Deaconess Medical Center. Analysis of the model under investigation shows that the disease-free equilibrium existing for all parameters is globally asymptotically stable when both and are less than one. We also carry out the sensitivity analysis to identify the most sensitive parameters for controlling the spread of the infection. Additionally, the solution for the above-mentioned model is obtained by the Laplace-Adomian decomposition method and various simulations are performed by using convenient fractional-order .
本研究详细阐述了使用卡普托分数阶算子的院内社区获得性耐甲氧西林金黄色葡萄球菌（CA-MRSA，一种新型耐甲氧西林金黄色葡萄球菌菌株）以及医院获得性耐甲氧西林金黄色葡萄球菌（HA-MRSA）。这两种被称为葡萄球菌的耐甲氧西林金黄色葡萄球菌菌株在医院中一直是严重问题，并且已知它们每年导致的死亡人数比艾滋病更多。因此，通过非局部分数阶导数分析了决定CA-MRSA是否会超过HA-MRSA的传播动力学。我们通过不动点定理证明了分数阶葡萄球菌感染模型解的存在性和唯一性。此外，通过递归过程提供了稳定性分析和迭代解。我们利用从贝斯以色列女执事医疗中心获得的参数值。对所研究模型的分析表明，当 和 都小于1时，对于所有参数存在的无病平衡点是全局渐近稳定的。我们还进行了敏感性分析，以确定控制感染传播的最敏感参数。此外，通过拉普拉斯 - 阿多米安分解法获得了上述模型的解，并使用方便的分数阶 进行了各种模拟。
