Word Count : 409

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हमारे पास महामारी का मॉडल इस अवकल समीकरण द्वारा दिया गया है: [ \frac{dx}{dt} = -\beta x (n + 1 - x) ] जहाँ (x(t)) सुग्राह्य व्यक्तियों की संख्या है, (\beta = 0.002), और प्रारंभ में (x(0) = n = 5000) है। i) जनसंख्या का घनत्व जब नए रोगी बनने की दर अधिकतम हो: नए रोगी बनने की दर: [ R(t) = -\frac{dx}{dt} = \beta x (n+1-x) ] अधिकतम दर तब होगी जब (dR/dx = 0)। [ R(x) = \beta x (n+1-x) = \beta (-x^2 + (n+1)x) ] [ \frac{dR}{dx} = \beta (-2x + (n+1)) = 0 ] [ -2x + (n+1) _____ _______ _______ ______ ___.
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