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Mathematical analysis for a new nonlinear measles epidemiological system using real incidence data from Pakistan

机译：基本巴基斯坦真正发病率数据的新非线性麻疹流行病学系统的数学分析

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摘要

Modeling of infectious diseases is essential to comprehend dynamic behavior for the transmission of an epidemic. This research study consists of a newly proposed mathematical system for transmission dynamics of the measles epidemic. The measles system is based upon mass action principle wherein human population is divided into five mutually disjoint compartments: susceptible S(t)-vaccinated V(t)-exposed E(t)-infectious I(t)-recovered R(t). Using real measles cases reported from January 2019 to October 2019 in Pakistan, the system has been validated. Two unique equilibria called measles-free and endemic (measles-present) are shown to be locally asymptotically stable for basic reproductive number R-0 < 1 and R-0 > 1, respectively. While using Lyapunov functions, the equilibria are found to be globally asymptotically stable under the former conditions on R-0. However, backward bifurcation shows coexistence of stable endemic equilibrium with a stable measles-free equilibrium for R-0<1. A strategy for measles control based on herd immunity is presented. The forward sensitivity indices for R-0 are also computed with respect to the estimated and fitted biological parameters. Finally, numerical simulations exhibit dynamical behavior of the measles system under influence of its parameters which further suggest improvement in both the vaccine efficacy and its coverage rate for substantial reduction in the measles epidemic.
机译：传染病的建模对于理解流行病传播的动态行为至关重要。该研究研究包括一种用于麻疹流行病的新提出的数学系统。麻疹系统基于大规模作用原理，其中人口分为五个相互脱节隔室：易感S（t）-Vaccated v（t） - 曝光e（t） - e（t） - 射出Ⅰ（t）-recovered r（t）。使用2019年1月至2019年10月在巴基斯坦的真实麻疹病例，该系统已被验证。两个称为麻疹和流行（麻疹存在）的独特均衡被显示为基本生殖数字R-0 <1和R-0> 1的局部渐近稳定。在使用Lyapunov功能的同时，在R-0的前一个条件下发现均衡在全球渐近稳定。然而，落后分叉显示稳定的流动平衡的共存，具有稳定的无麻痹平衡对于R-0 <1。介绍了基于畜群免疫力的麻疹控制策略。还相对于估计和拟合的生物参数计算R-0的前进敏感性指数。最后，数值模拟在其参数的影响下表现出麻疹系统的动态行为，进一步提出了疫苗疗效的改善及其在麻疹流行病中大幅减少的覆盖率。

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