Terefe Y A, Njagarah J B H, Kassa S M
Department of Mathematics and Applied Mathematics, University of the Free State, South Africa.
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana.
Math Comput Simul. 2023 Jun;208:444-479. doi: 10.1016/j.matcom.2023.01.040. Epub 2023 Feb 3.
The movement of persons during the pandemic has played a significant role in increasing the disease transmission rates as well as the spread of COVID-19 variants from one region to another. Although, strict restrictions on movement of persons across borders had been imposed early on in the pandemic, countries had to open up their borders to travel as a way of trying to resuscitate their economies that were declining due to closure of businesses and restriction on both local and international travel. Although the lifting of travel bans was done under strict regulations, there has since been a spike in the number of infection cases and spread of virus variants. These increases have certainly put a lot of strain on the rather limited resources allocated to fighting COVID-19 in most regions including the Eastern and Southern Africa. In this manuscript, we examine the potential role played by cross-border movements on the number of detected cases in a developing country. Here, we consider cases where persons cross borders through either designated controlled border points with proper facilitation for screening and detection of potentially infected cases, as well as border crossings through ungazatted points. The persons crossing borders are considered to be either susceptible, exposed or infected with no or mild symptom. A mathematical model was formulated to cater for the aforementioned classifications as well as additional important dynamics related to the disease. The behaviour of solutions for the model is determined and the conditions for existence of the disease free equilibrium as well as the disease persistent equilibrium ascertained. Finally, a dynamically consistent nonstandard finite difference scheme is proposed to replicate the properties of the continuous model. The baseline model was fitted to data of two waves, parameter values were determined and used to obtain numerical results. Our results show that, an increase in cross border movement can result in an increase in the number of detected cases. We observed that if the number of persons who cross-border points while positive for COVID-19 is reduced by 60%, the total number of detected cases can be reduced by up to 58%. In addition, an 83% increase in immigration of exposed persons can increase the disease burden in a destination country by at least 14%. These results justify border points closures during a pandemic or imposing very stringent measure across borders to curtail the importation of positive cases in a country.
疫情期间人员流动在提高疾病传播率以及将新冠病毒变种从一个地区传播到另一个地区方面发挥了重要作用。尽管在疫情早期就对人员跨境流动实施了严格限制，但各国不得不开放边境以恢复因企业关闭以及本地和国际旅行受限而衰退的经济。尽管旅行禁令的解除是在严格规定下进行的，但此后感染病例数量和病毒变种传播出现了激增。这些增长无疑给包括东非和南非在内的大多数地区用于抗击新冠疫情的相当有限的资源带来了巨大压力。在本手稿中，我们研究了跨境流动对一个发展中国家检测到的病例数所起的潜在作用。在此，我们考虑人员通过设有适当筛查和检测潜在感染病例设施的指定受控边境点跨境的情况，以及通过未设关卡地点的边境过境情况。跨境人员被视为易感染者、暴露者或无症状或症状轻微的感染者。构建了一个数学模型来考虑上述分类以及与该疾病相关的其他重要动态情况。确定了该模型解的行为，并确定了无病平衡以及疾病持续平衡存在的条件。最后，提出了一种动态一致的非标准有限差分格式来复制连续模型的性质。将基线模型拟合到两波数据，确定参数值并用于获得数值结果。我们的结果表明，跨境流动的增加会导致检测到的病例数增加。我们观察到，如果新冠病毒检测呈阳性时跨境的人数减少60%，检测到的病例总数可减少多达58%。此外，暴露者入境人数增加83%可使目的地国家的疾病负担至少增加14%。这些结果证明了在疫情期间关闭边境点或在边境实施非常严格的措施以减少一个国家阳性病例输入的合理性。
