In this dissertation we present the quantitative response of an epidemic of the so-called SIR-type, in a population consisting of a local component and a migrant component. Each component can be divided into three classes, the susceptible individuals, usually denoted by S, who are uninfected but may contract the disease, infected individuals (I) who are infected and can spread the disease to the susceptible individuals and the class (R) of recovered individuals. If a susceptible individual becomes infected, it moves into the infected class. An infected individual, at recovery, moves to the class R. Firstly we develop a model describing two interacting populations with vaccination. Assuming the vaccination rate in both groups or components are constant, we calculate a threshold parameter and we call it a vaccination reproductive number. This invariant determines whether the disease will die out or becomes endemic on the (in particular, local) population. Then we present the stability analysis of equilibrium points and the effect of vaccination. Our primary finding is that the behaviour of the disease free equilibrium depend on the vaccination rates of the combined population. We show that the disease free equilibrium is locally asymptotically stable if the vaccination reproductive number is less than one. Also our stability analysis show that the global stability of the disease free equilibrium depends on the basic reproduction number, not the vaccination reproductive number. If the vaccination reproductive number is greater than one, then the disease free equilibrium is unstable and there exists three endemic equilibrium points in our model. Two of these three endemic equilibria are so-called boundary equilibrium points, which means that the infection is only in one group of the population. The third one which we focus on is the general endemic point for the whole system. We derive a threshold condition that determines whether the endemic equilibria is locally asymptotically stable or not. Secondly, by assuming that the rate of vaccination in the migrant population is constant, we apply optimal control theory to find an optimal vaccination strategy in the local population. Our numerical simulation shows the effectiveness of the control strategy. This model is suitable for modeling the real life situation to control many communicable diseases. Models similar to the model used in the main contribution of our dissertation do exist in the literature. In fact, our model can be regarded as being in-between those of [Jia et al., Theoretical Population Biology 73 (2008) 437-448] and [Piccolo and Billings, Mathematical and Computer Modeling 42 (2005) 291-299]. Nevertheless our stability analysis is original, and furthermore we perform an optimal control study whereas the two cited papers do not. The essence of chapter 5 and 6 of this dissertation is being prepared for publication.
It is 1874 of the Imperial Era. The War of the West has ended after nearly six years. On one side, the Kingdoms of Aequor, Galenthia and Ryalta – the Allied Powers. On the other, the Principality of Kentaire and the Holy States of Rikton – the Central Powers. Friends came and went; Navali, once a Central Power shifted in 1869 to neutrality, in order to deal with other foes. The Free City State Four Corners, officially neutral, showered the Allies with men, money and material. A treaty of peace has been signed at the Senate of the West. Both Galenthia and Aequor have agreed to terms and Rikton has followed, though none are truly happy with the strength that their former foe, Kentaire, has maintained. Mistrust and intrigue are rife.
Still, the end of hostilities after years of war has at least salved some wounds and means that garrisons can replenish, fields that have laid fallow for years can be sowed, and business can resume. True to the traditions of the Civilised West, however, true peace continues to elude all. In the east, the Vir Sidus Empire has nearly crumbled under the onslaught of the vicious Qatunax, who've pushed even into Aequor and Galenthia, carving out new lands for their High King. The goblins, their masters and whatever other creatures lurk in the Ergonian mountains are a constant threat, with the wilds of the borders becoming dangerous and unpredictable. In the far west, the mysterious sea borne Mitanga occasionally probe, while White Hall's fierce Ice Clans pillage and plunder the west coast of the civilised kingdoms and in the south, both the Empire of Partharia and the Principality of Alezzo wait for their chances to strike.
The winds blew and with them came the Empire of Partharia. At this moment most of the Fortresses on the Great Salt are under Siege. If you could not be in the 7 Oct battle but are a regular resident of one of the Fortresses, please put up a memoir about being, Under Siege. They did not use military ships to accomplish this. They literally flooded the Great Salt with Merchant Ships hauling huge numbers of Slaves and Client Kingdom soldiers.
Which to the educated mind means that the long delay before the attack was setting this up, and frankly GETTING all these ships and that the REAL Military hasn't arrived yet. Those of the Military Ships and their professional Soldiers.
A Social. On the walls looking at the enemy. Taunting them. Whatever. Even in the local Drinking Hole. Thanks to Dertan and Thomas, the Fortresses are VERY well supplied. So have a Pint and comisserate.
A skirmish on the walls. Just don't have it be in the neighborhood of thousands, but a hundred or so is fine.
Scout the area around the fortress. Feel free to run these for yourselves. Remember this is COOPERATIVE Storytelling. Tell a good story! But don't forget the drama and challenge. You are the Heroes of this tale, but you are NOT batman or superman. You can fail, and should sometimes!
Airships are NOT running in Southern Aequor, or along the Coast. At All. At present. Which means if you want to travel in those areas speak to a Staffer. The East (ie Hellsmouth and Rhone is still being serviced)
Similarily, because they pass over the Coast, Airships are NOT traveling to Navali, or Ryalta. You can still get to Four Corners but it takes a very round about way that does not touch the coast.
FS3 no longer in use - FATE Crusade is the new system! Please see the link here, which will explain the rudiments of the system until we get a fully functioning page up. This page has skill, chargen and combat info.
Please bear with us while we work through everything and fully establish FATE in Eternal Crusade, and let us know if you have any issues.
FATE Crusade This is the new system. Please bear in mind there is LOTS of dust as we tweak and correct it so as to make it even better for our players. This page currently houses everything for FATE Crusade including: Chargen, Skill lists, Stunt suggestions, commands in game.
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Flee from hate, mischief and jealousy. Don't bury your thoughts, put your vision to reality. Wake Up and Live!... እውነት ይከበር።