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S1, s2, s2, s4, …….. sn Nt = St + Lt + RtNt = St + ltL1, l2, l3, l4 ,…………….lndstdt= -β st ltdltdt= β st lt – yltdRtdt= ylt∫β(t)dS(t−ɽ)dtdɽ= β( N – Lt) Lt – yLt= βNLt – βL2t – yLt= (βN – y)lt– βl2t - ylt= ¿dltdt=¿(βN – y) lt - βL2tThe derivative of I = It = 1ydltdt=1y2dydt1y2=dydt= (βN – y) 1y-β1y2dydt= (βn – Y) Y – β
CORONA VIRUS MODELLING IN THE U.S. A5¿dydt+¿βn -y)y = βDetermine the optimal vaccination strategyThe solution is calculated using S.I.R∫−∞qdπ2.3^0 = 22.3^1 = 2.22.3^2 = 5.342.3^3 = 12.662.3^4 = 27.222.3^5 = 64.3612βN – Y = 0βN – Y ≠ 0βN – Y < 0βN – Y > 0It= 11lo+βtIt= β N−Ye(β N−Y)t1lo+β¿(e(β N−Y)t−1)¿Nβy>1
CORONA VIRUS MODELLING IN THE U.S. A6Nβ = No. of people infected per unit time.Reproduction number, R0= Nβy1y=the average lengthof time∈infected compartmentR0 > 1 – epidemicAttack ratio = 1 - S∞NApril will have 89 casesTask 2Total number of covid – 19 cases according to the formula of summation notation is = = ∑i=otcRoi+1lc∑i=1t−tcReiThe control can be effective when there is controlled spread. Task 2bFind the limiting value capacity (carrying capacity). Interpret this value in this contextTo calculate the limiting value also known as the carrying capacity, then we must calculate the 95% confidence level.Change over a day = E. P. NdNd + 1 = Nd + E.p. NdNd + 1 = Nd + E. p. NdNd + 1 = (1 + E.P.Nd
CORONA VIRUS MODELLING IN THE U.S. A7Nd + 1 = (1 + E.P)NdNd = (1 + E.p)d. NoNd – number of cases per dayE = average number of people an infected person is exposed to per dayP = probability of the exposure becoming an infectionUsing the Logistic curve2.3^0 = 12.3^1 = 2.32.3^2 = 5.292.3^3 = 12.172.3^4 = 27.982.3^5 = 64.36April will have 122 cases.TaskPrediction of the total number of Covid – 19 cases in 30thApril 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