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

A. Ssematimba, J. N. Nakakawa, J. Ssebuliba, J. Y.T. Mugisha

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1358-1369
Number of pages12
JournalInternational Journal of Dynamics and Control
Issue number4
Early online dateMar 13 2021
StatePublished - Mar 13 2021
Externally publishedYes

Bibliographical note

Funding Information:
The authors acknowledge and thank the Government of Uganda and Makerere University Research and Innovation Fund for the grant to carry out this study, and Ministry of Health for the data on COVID-19.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • COVID-19
  • Critical area
  • Crowding
  • Mathematical modelling
  • Standard operating procedures


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