Question

Question 1. 50 points

Here we want to model the spread of the COVID-19 epidemic!

Assume that ENCE112 Country get it first infection from a gentleman who flew in from China-Town, Wuham. Assume also that each without isolation, any covid-19 patient infects one other person. If we assume that each covid-19 infected person is isolated after just one day.

a. Derive a recursive formula for the number of infected persons in n-days. 10 points

b. Develop a recursive algorithm for the formula you derived in “a.” above. 15 points

c. Translate the algorithm in “b.” above into C programming language and run it. 5 points

d. Generate the results of the first ten (10) days in a table of two columns, the first column holds the days and the second column holds the number of infected persons. 10 points

e. What will happy if each covid-19 patient infects more than one person per day before isolation? Repeat “d.” if the infection rate is two (2) instead of one. 10 points

Question 2. 50 points

We want to solve this program analytically and plot it and compare it to the discrete solution

above in Question 1.

Here we model the problem as a deferential equation. So the rate of infection is a function of the number of infected persons:

???? =??????????????????????? ??? ? ?? ?h? ???? ?? ?????????? ?? ????

Then we say that

dx = ??, where ? is constant signalling the number persons infected by each patient dt

a. Solve this equation with initial conditions of ? = 1 when ? = 0 10 points

b. For the case of ? = 1 write a simple C- program to compute the number of infections

for each day and generate a similar table as in Question 1 (d.) above. 10 points

c. Write a simple C-program to plot the points of the table with the days on the vertical

axis and the number of infections on the horizontal axis using “*”. Note: (0,0) is the upper left corner of the plot window! 30 points

Answer 1

model for COVID-19 epidemic
given that any covid-19 patients infects one other person
that is fist infect to -> second -> third so on.
also given that covid-19 infected person is isolated after just one day.
that is first person can not infect more then one person.
so our recursive formula is that
f(n) = f(n-1) + 1 where f(1) =1 and n is after number.
simple game of triangle
c Program for the child triangle game.
Program file is 'triangle.c'
#include <stdio.h>

// find the maximum stick
int maxStick(int *a,int *b,int *c){
// check c is maximum
if(*c>=*b && *c>=*a){
// swap max to a stick
int temp =*c;
*c=*a;
*a=temp;
}
//check b is maximum
else if(*b>=*a && *b>=*c){
int temp =*b;
*b=*a;
*a=temp;
}
return *a;
}

// determine form a triangle from stick
int formTriangle(int a,int b,int c){
// single test to check
// c programming not support boolean so use 0 and 1 for indication
if(b+c > a)
return 1;
else
return 0;
}

// determine angle
void checkAngle(int a,int b,int c){
// because it triangle form and sum of all angle is pi(180)
printf("all the three angle of triangle are < pi\n");

// check for one angle >pi/2
if(a*a > b*b +c*c)
printf("One angle > pi/2\n");
// check for one angle = pi/2
else if(a*a == b*b +c*c)
printf("One angle = pi/2\n");
}

int main(){
printf("Enter the length of three stick :");
int a,b,c;
scanf("%d%d%d",&a,&b,&c);

// call function to find max stick
printf("Largest stick is %d\n",maxStick(&a,&b,&c));
  
if(formTriangle(a,b,c)){
printf("True\n");
checkAngle(a,b,c);
}
else
printf("False\n");

return 0;
}