State two real-world problems where you think that mathematical

Question

State two real-world problems where you think that mathematical modelling is the only approach to find the solution of the problem. Give 4 essentials for each of the problems. Why do you think that there is no other scientific alternative for the treatment of these problems.
b) Classify the following into linear and non-linear models, justifying your classification.

i) Simple harmonic motion for small amplitude of oscillation.

ii) Population growth model given by

$$\frac{dN}{dt} = aN (B - kN), \text{ a, B, k are constants.}$

iii) Equation for velocity v of a particle at any time t, moving with a constant acceleration a, and initial velocity u.

iv) Equation describing dynamic stability of market equilibrium price given by

$$p_t = [1 + k(a - A)p_{t-1} + k(b - B)], \text{ a, b, A, B, k are constants}$ $

and p_t is the price in period t.

09 Jan 2026

Answer :

Word Count : 423

One real-world problem where mathematical modelling is essential is epidemic spread prediction. To control and prevent infectious diseases like COVID-19 or influenza, mathematical models such as SIR (Susceptible-Infected-Recovered) are used. The four essentials for this problem are: 1. Population data – total population, initial infected, and susceptible individuals. 2. Transmission rate – how quickly the disease spreads per contact. 3. Recovery rate – rate at which infected individuals recover or ____ _____ ____ ____ _________ _______ _____ ______ __________ __________ ______.
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