Coronavirus (COVID-19) Modeling the Outbreak SM Garba and JM-S - PowerPoint PPT Presentation

Coronavirus (COVID-19) Modeling the Outbreak SM Garba and JM-S Lubuma Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa. Biomath coffee February 25, 2020. Biomath coffee (UP) COVID19 1 / 11

Exponential growth of cases & 26 & 12 01 Feb 20 23 Feb 20 15 Feb 20 Biomath coffee (UP) COVID19 2 / 11

Pandemic situation Biomath coffee (UP) COVID19 3 / 11

https://youtu.be/mOV1aBVYKGA present data don’t inform the direction of transmission; Original source is unknown ; There is no vaccine or specific antiviral treatment. Widen consequences include: potential economic instability; Biomath coffee (UP) COVID19 4 / 11

https://youtu.be/mOV1aBVYKGA present data don’t inform the direction of transmission; Original source is unknown ; There is no vaccine or specific antiviral treatment. Widen consequences include: potential economic instability; xenophobia and racism against Chinese and Asians. Biomath coffee (UP) COVID19 4 / 11

Current control measures The main control measures applied include: Quarantine of; Cruise ships in Japan water and nearby China; Carfew of over 170million people in China. Isolation of individual with clinical symptoms; Body temp check in major airports and trains around the world; warning against travel to China. Biomath coffee (UP) COVID19 5 / 11

Current control measures The main control measures applied include: Quarantine of; Cruise ships in Japan water and nearby China; Carfew of over 170million people in China. Isolation of individual with clinical symptoms; Body temp check in major airports and trains around the world; warning against travel to China. xenophobia and racism against Chinese and Asians. Biomath coffee (UP) COVID19 5 / 11

Flow diagram of the Model Biomath coffee (UP) COVID19 6 / 11

Model Equations dS dt = Π + α q + σ (1 − p ) Q − ( λ + µ ) S , dE dt = α (1 − q ) + λ S − ( τ 1 + τ 2 + µ ) E , dI dt = τ 1 E − ( γ + ν 1 + δ 1 + µ ) I , (1) dQ dt = τ 2 E − ( σ + µ ) Q , dJ dt = γ I − ( ν 2 + δ 2 + µ ) J , dR dt = δ 1 I + δ 2 J + σ pQ − µ R , with λ = β ( I + η 1 E + η 2 Q + η 3 J ) N . Biomath coffee (UP) COVID19 7 / 11

Existence of Equilibria Lemma The model (1) , has no disease free equilibrium (q � = 1 in exposed class). we define an invasion threshold R = β (Π+ α )[ τ 1 K 3 ( K 4 + η 3 γ )+ K 2 K 4 ( η 1 K 3 + η 2 τ 2 )] . K 1 K 2 K 3 K 4 (Π+ α q ) Theorem Model (1) has: (i) a unique endemic equilibrium for all values of R if q ∈ [0 , 1) and α > 0 , (ii) a unique EE if R > 1 and either q = 1 or α = 0 , (iii) no EE if R < 1 and either q = 1 or α = 0 . Biomath coffee (UP) COVID19 8 / 11

Quarantine and Isolation Strategies ◮ Investigated via threshold analysis approach on R c | ( τ 2 ,γ ) ; ◮ for Quarantine: d R c = βη 2 − β [ K 2 K 4 ( η 1 K 3 + η 2 τ 2 ) + τ 1 K 3 ( K 4 + η 3 γ )] (2) , K 2 d τ 2 K 1 K 2 1 K 2 K 3 K 4 from (2) 2 = η 1 K 2 K 3 K 4 + τ 1 K 3 ( K 4 + η 3 γ ) η ∗ . K 2 K 4 ( τ 1 + µ ) Therefore, d R c ≶ 0 iff η 2 ≶ η ∗ 2 . d τ 2 Biomath coffee (UP) COVID19 9 / 11

Quarantine and Isolation Strategies ◮ Investigated via threshold analysis approach on R c | ( τ 2 ,γ ) ; ◮ for Quarantine: d R c = βη 2 − β [ K 2 K 4 ( η 1 K 3 + η 2 τ 2 ) + τ 1 K 3 ( K 4 + η 3 γ )] (2) , K 2 d τ 2 K 1 K 2 1 K 2 K 3 K 4 from (2) 2 = η 1 K 2 K 3 K 4 + τ 1 K 3 ( K 4 + η 3 γ ) η ∗ . K 2 K 4 ( τ 1 + µ ) Therefore, d R c ≶ 0 iff η 2 ≶ η ∗ 2 . d τ 2 ◮ Similarly for Isolation: d R c ≶ 0 iff η 3 ≶ η ∗ 3 . d γ Biomath coffee (UP) COVID19 9 / 11

Proposition The use of quarantine of the exposed individuals will have positive (negative) impact in a community if η 2 ≶ η ∗ 2 . Biomath coffee (UP) COVID19 10 / 11

Proposition The use of quarantine of the exposed individuals will have positive (negative) impact in a community if η 2 ≶ η ∗ 2 . Similarly, Proposition The use of isolation of infectious individuals will have positive (negative) impact in a community if η 3 ≶ η ∗ 3 . Biomath coffee (UP) COVID19 10 / 11

Research Objectives To assess the transmission dynamics of CoVID-19 for future predictions. To determine the impact of Quarantining and Isolation strategies in controlling the disease. More questions to come ????????? Biomath coffee (UP) COVID19 11 / 11

Thank you for your attention Biomath coffee (UP) COVID19 12 / 11