S1 s2 s2 s4 sn Nt St Lt RtNt St ltL1 l2 l3 l4 ln dst dt \u03b2 st lt dltdt \u03b2 st lt

# S1 s2 s2 s4 sn nt st lt rtnt st ltl1 l2 l3 l4 ln dst

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S1, s2, s2, s4, …….. sn Nt = St + Lt + Rt Nt = St + lt L1, l2, l3, l4 ,…………….ln dst dt = -β st lt dlt dt = β st lt – ylt dRt dt = ylt β ( t ) dS ( t ɽ ) dt d ɽ = β( N – Lt) Lt – yLt = βNLt – βL 2 t – yLt = (βN – y)l t – βl 2 t - yl t = ¿ dlt dt = ¿ (βN – y) lt - βL 2 t The derivative of I = It = 1 y dlt dt = 1 y 2 dy dt 1 y 2 = dy dt = (βN – y) 1 y - β 1 y 2 dy dt = (βn – Y) Y – β
CORONA VIRUS MODELLING IN THE U.S. A 5 ¿ dy dt + ¿ βn -y)y = β Determine the optimal vaccination strategy The solution is calculated using S.I.R q 2.3^0 = 2 2.3^1 = 2.2 2.3^2 = 5.34 2.3^3 = 12.66 2.3^4 = 27.22 2.3^5 = 64.3612 β N – Y = 0 β N – Y ≠ 0 β N – Y < 0 β N – Y > 0 I t = 1 1 lo + βt I t = β N Y e ( β N Y ) t 1 lo + β ¿ ( e ( β N Y ) t 1 ) ¿ N β y > 1
CORONA VIRUS MODELLING IN THE U.S. A 6 Nβ = No. of people infected per unit time. Reproduction number, R 0 = N β y 1 y = the average lengthof time infected compartment R0 > 1 – epidemic Attack ratio = 1 - S∞ N April will have 89 cases Task 2 Total number of covid – 19 cases according to the formula of summation notation is = = i = o tc Roi + 1 lc i = 1 t tc Rei The control can be effective when there is controlled spread. Task 2b Find the limiting value capacity (carrying capacity). Interpret this value in this context To calculate the limiting value also known as the carrying capacity, then we must calculate the 95 % confidence level. Change over a day = E. P. Nd Nd + 1 = Nd + E.p. Nd Nd + 1 = Nd + E. p. Nd Nd + 1 = (1 + E.P.Nd
CORONA VIRUS MODELLING IN THE U.S. A 7 Nd + 1 = (1 + E.P)Nd Nd = (1 + E.p) d . N o Nd – number of cases per day E = average number of people an infected person is exposed to per day P = probability of the exposure becoming an infection Using the Logistic curve 2.3^0 = 1 2.3^1 = 2.3 2.3^2 = 5.29 2.3^3 = 12.17 2.3^4 = 27.98 2.3^5 = 64.36 April will have 122 cases. Task Prediction of the total number of Covid – 19 cases in 30 th April 2020. Finding the solution for this pandemic should come as soon as possible. It is possible to understand why staff and researchers working at disease control agencies such as Centre for Disease Control (CDC), epidemiologist among others are worried. More than 3, 433 Americans

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• Fall '19
• Logistic function, S-I