Abstract
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.