Mathematical model for COVID-19 management in crowded settlements and high-activity areas

• Published in: International journal of dynamics and control 2021, Vol.9 (4), p.1358-1369
• Main Authors: Ssematimba, A., Nakakawa, J. N., Ssebuliba, J., Mugisha, J. Y. T.
• Format: Article
• Language: English
• Subjects: Churches; Complexity; Control; Control and Systems Theory; Coronaviruses; COVID-19; Disease control; Disease transmission; Dynamical Systems; Engineering; Mathematical analysis; Mathematical models; Population density; Vibration
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-021-00781-9

This paper develops and analyses a habitat area size dependent mathematical model to study the transmission dynamics of COVID-19 in crowded settlements such as refugee camps, schools, markets and churches. The model quantifies the potential impact of physical/social distancing and population density on the disease burden. Results reveal that with no fatalities and no infected entrants, the reproduction numbers associated with asymptomatic and symptomatic cases are inversely proportional to; the habitat area size, and the efforts employed in tracing and hospitalising these cases. The critical habitat area below which the disease dies out is directly proportion to the time taken to identify and hospitalise infected individuals. Results also show that disease persistence in the community is guaranteed even with minimal admission of infected individuals. Our results further show that as the level of compliance to standard operating procedures (SOPs) increases, then the disease prevalence peaks are greatly reduced and delayed. Therefore, proper adherence to SOPs such as use of masks, physical distancing measures and effective contact tracing should be highly enforced in crowded settings if COVID-19 is to be mitigated.