Investigating the impact of isolation, self-isolation and environmental transmission on the spread of COVID-19: Case study in Rwanda

• Autorzy: Lubuma Jean M.-S. , Tassé Arsène Jaures Ouemba , Signing Francis , Tsanou Berge

Identyfikatory

DOI

10.14708/ma.v51i2.7212

Warianty tytułu

PL

Badanie wplywu izolacji, samoizolacji i transmisji srodowiskowej na rozprzestrzenianie sie COVID-19 : Studium przypadku w Rwandzie

• Języki publikacji: EN

Abstrakty

EN

In this work, we propose a ten-compartmental COVID-19 model with human to human and environment to human transmissions. A notational feature of this model is the consideration of the infected who escape from the self–isolation and later spread the disease. The model is rigorously analysed both theoretically and numerically. From the mathematical point of view, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R is less than one, that is the disease dies out. When R is greater than one, we prove that the model admits a unique endemic equilibrium, locally asymptotically stable, meaning that the disease would persist, at least inside the basin of attraction of the endemic equilibrium. The sensitivity analysis of the model highlights that the environmental transmission is the most influent parameter, which leads in an increasing number of infected individuals whenever it increases. The model is calibrated using the daily cumulative asymptomatic cases in Rwanda reported from the 1 April 2022 to the 14 June 2022. We found that the basic reproduction number is equal to 0.6479 and most infected people in Rwanda during this period of time are asymptomatic. We investigate the impact of isolation and self-isolation to reduce the disease burden, and both sensitivity analysis and numerical analysis show that the isolation has more effect on the dynamics of the infected than the self-isolation. We also prove that, the individuals who escape from the self-isolation, contribute, but weakly to the increasing of the number of infected individuals.

PL

W niniejszej pracy proponujemy dziesiecioprzedzialowy model COVID19 z transmisja z czlowieka na czlowieka i ze środowiska na człowieka. Istotną cechą tego modelu jest uwzglednienie zarażonych, którzy uciekają z samoizolacji, a następnie rozprzestrzeniają chorobę. Model jest rygorystycznie analizowany zarówno teoretycznie, jak i numerycznie. Z matematycznego punktu widzenia udowadniamy, że stan wolny od choroby jest globalnie asymptotycznie stabilna, gdy Rav₀^av jest mniejsze niz jeden, czyli choroba wymiera. Gdy Rav jest wieksze niz jeden, udowadniamy, że model dopuszcza unikalną równowagę endemiczna, lokalnie asymptotycznie stabilną, co oznacza , że choroba utrzyma się, przynajmniej wewnatrz basenu przyciągania równowagi endemicznej. Analiza wrażliwości modelu podkreśla, że transmisja środowiskowa jest najbardziej wpływowym parametrem, który prowadzi do rosnącej liczby zarażonych osobników, gdy tylko wzrasta. Nasz model został skalibrowany przy użyciu dziennych skumulowanych przypadków bezobjawowych w Rwandzie zgłoszonych od 1 kwietnia 2022 do 14 czerwca 2022. Stwierdziliśmy, że współczynnik odnowienia choroby jest równy 0, 6479, a wiekszość zarazonych osób w Rwandzie w tym okresie jest bezobjawowa. Badamy wpływ izolacji i samoizolacji w celu zmniejszenia obciążenia chorobą, a zarówno analiza wrażliwosci, jak i analiza numeryczna pokazują, ze izolacja ma większy wpływ na dynamikę infekcji niż samoizolacja.

Słowa kluczowe

EN

COVID-19; Isolation; Environmental transmission; Stability of equilibria; Sensitivity

PL

Izolacja; Samoizolacja; Transmisja środowiskowa; Uciekinier; Globalna stabilność; Analiza wrażliwości

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2023
• Tom: Vol. 51, no. 2
• Strony: 239--271
• Opis fizyczny: Bibliogr. 28 poz., tab., wykr.

Twórcy

autor

Lubuma Jean M.-S.

• University of the Witwatersrand Johannesburg School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg, South Africa

• https://orcid.org/0000-0002-1654-9298

autor

Tassé Arsène Jaures Ouemba

• University of the Witwatersrand Johannesburg School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg, South Africa
• Mony Keng Higher Institute, Bafoussam, Cameroon

autor

Signing Francis

• Department of Mathematics and Computer Science University of Dschang, Cameroon

autor

Tsanou Berge

• Department of Mathematics and Computer Science University of Dschang, Cameroon
• Department of Mathematics and Applied Mathematics University of Pretoria, South Africa

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).

Autorzy nr 2, 3 i 4 z błędnie przypisanymi w pdf ORCIDami.