How to divide the stolen gold bars? Five robbers, Adam, Bob, Chuck, Dave and Eric (ordered by the level of experience, with Eric being the most experienced), just robbed a bank and stole 100 gold bars. Now they are hiding in a cave, where there are hungry wolves roaming outside. The key problem they need to resolve is how to split the gold bars among themselves. After a long grueling debate, they settle on the following process for determining how to split the fortune: starting from Eric (and follow the decreasing order of experience), each time one person proposes a way to split the gold bars among all (surviving) robbers. For example, Eric could propose to give himself 60 bars, and give each of the rest 10 bar each. If at least half (yes the one proposing the plan is counted) of the remaining guys agree to the proposed way of splitting the gold bars, that is the final way of splitting the fortune and the process stops; otherwise, the one who just proposed the splitting plan must leave the cave (and will surely be eaten by the wolves) and then the process continues. Now imagine you are Eric. Tell me what you are going to propose the way of splitting the fortune. You need to justify your answer. Note: you can assume each person is selfish and logical: each wants to be alive and at the same time he wants the maximum amount of gold bars. In case you still have energy left after working on this homework, you can think about the following questions: what if there are k = 6, 7, ... robbers? is it always better to be the first to propose a splitting method? If not, how many robbers will there be in that case? You don\'t need to answer these and no solutions will be given for these questions. But if you answer these correctly, you get 5% extra credits. Solution We are 5 people in an order of more experience to least experience to propose a solution. We all are selfish and all think logically. What solution i am going to propose is Give me 100 Golder bars so that, this process ends with me and you all people will servive. I am only telling this to the next you three people in the queue because, the least experied person will get the chance of proposing solution at the last so, he will definitely survive and he will get all 100 golden bars at the last. So the least experied guy is hundred percent safe. If you three people don\'t agree then what happens next is I will be sent out of this cave and i will die. The next person in the queue will propose the same offer because, he is also selfish ans he also wants more number of golden bars. Any way the least experied person won\'t agree because he is already saved with his life and will be given all 100 golden bars at the last. The remaining two people in the queue won\'t agree So, he will be sent out. Finally, the last two persons in the queue will be remaining. Chance comes to the fourth guy in this queue. Whatever the solution the fourth guy propose the fifth guy in the queue won\'t accpet because the p.

1. How would an SIR model need to be changed if the disease in question were universally lethal?
How would this affect the pathogen’s ability to spread? Figure 3: An SIR(S) compartment model
showing the transmission rate B, The recovery rate y, the immunity loss rate o, and death birth
rates u, and u*. For lifelong immunity (o 0) this reduces to an SIR models. For a 0 is an SIRS
model.
Solution
If the disease was universally lethal then there would be no recovery in the model and eventually
the pathogen would wipe out the species