This was already happening before Steve Jobs health declined. Android went from 5% market share to 25% market share while Mr. Jobs was still in charge, making decisions and visibly in charge of the company.
What we are seeing with Tim Cook is just a continuation of the direction Google was already going. It's just a simple factor economics.
1. There are more companies making phones with Android, thus more competition which leads to lower prices.
2. Android phones in general are heavily subsidized by the mobile providers (Verizon, AT&T, T-Mobile, etc) and as such they have always been less expensive than Apple products.
So with those two points, consider the good old economic fact ... Lower Price = Greater Sales, now consider that the market is in transition. Apple had a head start, but it was early in the smartphone markets life, only 40-50 million people had smartphones at that point. The remainder of the 150 million phone in the US that were going to switch from old phones to smartphones did so when Apple had to compete against the less expensive phones. So as the smartphone market grew, Android took the greater number of sales thus Android's market share increased with the market and Apples started to shrink. The other factor in this is that Apple sells 70% to repeat customers, that means that only 30% of their sales are to new customers. So when you hear about the iPhone 5 selling 5 million units, only 1.5 million of those were to new converting customers or customers leaving other smartphone options. The other 3.5 million were people trading out an iPhone 3GS or iPhone 4 for the 5. Consistent customers are not a bad thing (companies kill for this), but it shows that the price point of Apples products are scaring off the new customers.
Case in point iPad Mini $320, Amazon Fire HD $200, Galaxy Nexus 7 $200. So when a parent is looking to buy that Christmas gift, what do you think they would rather shell out $200 or $320 when they get close to the same product.
Apple needs to look at history, this is the same thing that happened in the 80's-90's. They had one of the largest market shares for personal computers in the 80's at about 15%, the other 85% was carved up into little chunks by 10 to 20 companies so very few were as big as Apple. From 1985 to 1995 they went from 15% to 3%, and x86 PC's (running dos/windows) went from 5% to 95% of the market. PC's had multiple manufacturers (IBM, Wang, DEC, Compaq, HP, Packard Bell, etc) w/ a common operating system (dos/windows) = higher competition, lower prices.
The smartest move that Apple could do right now is open up their OS's to run on other manufacturers hardware. They have a strong footing in the market, they have 100 billion dollars, their current method of selling strictly high priced hardware/software is not a long term strategy. They should open it up so that other hardware manufacturers can build machines that run Mac OSX, or phones that run iOS. At the end of the day Apple could make money on licensing the OS's, and all of those new customers would drive more traffic to iTunes (this is the real cha-ching).