Barik Mamta, Chauhan Sudipa, Misra Om Prakash, Goel Shashank
Department of Mathematics, JIMS Engineering Management Technical Campus, Greater Noida, U.P India.
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada.
J Eng Math. 2023;139(1):3. doi: 10.1007/s10665-023-10264-9. Epub 2023 Apr 11.
Flu, a common respiratory disease is caused mainly by the influenza virus. The Avian influenza (H5N1) outbreaks, as well as the 2009 H1N1 pandemic, have heightened global concerns about the emergence of a lethal influenza virus capable of causing a catastrophic pandemic. During the early stages of an epidemic a favourable change in the behaviour of people can be of utmost importance. An economic status-based (higher and lower economic class) structured model is formulated to examine the behavioural effect in controlling influenza. Following that, we have introduced controls into the model to analyse the efficacy of antiviral treatment in restraining infections in both economic classes and examined an optimal control problem. We have obtained the reproduction number along with the final epidemic size for both the strata and the relation between reproduction number and epidemic size. Through numerical simulation and global sensitivity analysis, we have shown the importance of the parameters and on reproduction number. Our result shows that by increasing , and by decreasing , and , we can reduce the infection in both the economic group. As a result of our analysis, we have found that the reduction of infections and their level of adversity is directly influenced by positive behavioural patterns or changes as without control susceptible population is increased by , the infective population is decreased by and the recovered population is increased by in the higher economic group who opted changed behaviour as compared to the lower the economic group (people living with normal behaviour). Thus normal behaviour contributes to the spread and growth of viruses and adds to the hassle. We also examined how antiviral drug control impacts both economic strata and found that in the higher economic strata, the susceptible population increased by , the infective population decreased by and the recovered population improved by as compared to the lower economic group, the susceptible population has increased by , the infective population is decreased by and the recovered population is improved by . Our results enlighten the role that how different behaviour in separate socio-economic class plays an important role in changing the dynamics of the system and also affects the basic reproduction number. The results of our study suggest that it is important to adopt a modified behaviour like social distancing, wearing masks accompanying the time-dependent controls in the form of an antiviral drug's effectiveness to combat infections and increasing the proportion of the susceptible population.
流感是一种常见的呼吸道疾病，主要由流感病毒引起。禽流感（H5N1）疫情以及2009年H1N1大流行，加剧了全球对可能引发灾难性大流行的致命流感病毒出现的担忧。在疫情早期，人们行为的有利变化可能至关重要。构建了一个基于经济状况（高经济阶层和低经济阶层）的结构化模型，以研究控制流感方面的行为影响。随后，我们在模型中引入控制措施，分析抗病毒治疗在抑制两个经济阶层感染方面的效果，并研究了一个最优控制问题。我们得到了两个阶层的再生数以及最终疫情规模，以及再生数与疫情规模之间的关系。通过数值模拟和全局敏感性分析，我们展示了参数对再生数的重要性。我们的结果表明，通过增加以及减少、和，我们可以减少两个经济群体中的感染。我们的分析结果发现，感染及其严重程度的降低直接受到积极行为模式或变化的影响，因为在选择改变行为的高经济群体中，与低经济群体（行为正常的人群）相比，在没有控制的情况下，易感人群增加了，感染人群减少了，康复人群增加了。因此，正常行为有助于病毒的传播和增长，并增加了麻烦。我们还研究了抗病毒药物控制如何影响两个经济阶层，发现与低经济群体相比，在高经济阶层中，易感人群增加了，感染人群减少了，康复人群增加了，在低经济群体中，易感人群增加了，感染人群减少了，康复人群增加了。我们的结果揭示了不同社会经济阶层的不同行为在改变系统动态以及影响基本再生数方面所起的重要作用。我们的研究结果表明，采取如社交距离、佩戴口罩等改变后的行为，同时结合抗病毒药物有效性形式的时间依赖性控制措施，以及增加易感人群的比例，对于抗击感染非常重要。
