Question

QUESTION 1

a) It is now known the average rate of infection from the spread of corona virus endemic in a certain city daily is 2. Assume a suitable distribution to model the process.

b) Write a matlab program for model the probability of infection for the next 15 days.

c) Run as simulated plot for the Probability distribution and Cumulative distribution from the program above.

d) Using Simulation model estimate the probability that 3 people will infected in the next two days.

QUESTION 2

a) i) Based on a graph of the probability distribution (Q1d) indicate the probability that 3 persons will contract the virus in a given day

ii) Find the mean and standard deviation of the number of infections from (Q1) in the past three days.

b) The recent global climate change has necessitated the need for a new model for predicting weather patterns. Two scientists who were modeling this process in Ghana ended up with two different system models.

i) What could be the possible reason(s) for the differences in their system model? Justify your answer.

ii) In relation to real world data from the process how can you select the best model to employ for subsequent simulations and prediction of the process?

QUESTION 3

We wish to model the blood type of a person. It is known that blood type is inherited. If both parents carry genes for the AS and AS blood types, each child has probability 0.3 of getting two S genes and so of having blood type SS. Different children inherit independently of each other.

a) Write a Matlab program to determine the probability that the first child these parents have with type SS blood is their fifth child.

b) In relation to the three classifications of mathematical models, discuss the given genetic modelling problem in 2(a).

c) The administration of the Kasoa Government hospital wants to improve its quality of service by reducing the waiting time of travelers. For that purpose, they want to design what could be the best queuing strategy to have the minimum waiting time. You have been task to advice on the best queuing strategy in order to reduce the waiting time of patients before attended to. Discuss how you will address the problem

Answer 1

QUESTION 1 :

You can change infection rate (transmission rate) and see how spread is affected (flatten the curve).

Infection rate = beta = number of social contacts x probability of contracting virus each contact. When we socially isolate we reduce beta and therefore spread.

An individual is infectious for approximately 7 days. During this time they pass covid19 to approximately 2.5 people. These 2 basic parameters determine the model dynamics.

Simulink model is of the following system of three odes:

dS/dt = -β(I/N)S
dI/dt = β(I/N)S – γI
dR/dt = γI

S = Number Susceptible Individuals
I = Number Infectious Individuals
R = Number Recovered Individuals
N= Total Population
β = Ep = Number Social contacts x probability of transmitting disease each contact = Infection rate
γ = Recovery Rate

Key scenarios of dynamics:
If, during 7 days of being infectious, a person passes to 1 person then the disease will not grow, i.e., number of infectious individuals stays the same.
If, during 7 days of being infectious, a person passes to 2 or more people the disease grows, i.e., number of infectious individuals grows.
If, during 7 days of being infectious, a person does not pass to another person (or, say 10 people are sick at exact same time and pass to 9 people over 7 days) the disease will reduce, i.e., number of sick individuals goes to zero.
As individuals recover, the number of susceptible people decline, and therefore spread slows and eventually reduces to zero

QUESTION 3 :

a) For this first 4 children should not have blood type SS, the probaility being 0.7 and the fifth child should have blood type SS, the probability being 0.3.

Hence the answer is 0.7* 0.7* 0.7* 0.7*0.3

Matlab program:

p = 1;

i=1;

while i<=5

if i==5

p = p*0.3;

else

p = p*0.7;

end

i=i+1;

end

disp(p)

Please refer to the screenshot of the code to understand the indentation of the code

OUTPUT :

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