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The base current increase (decrease) is due to an increase (decrease) in vBE.
The increase (decrease) in vBE increases (decreases) the injection of carriers from the heavily doped emitter.
Most of these carriers cross the thin base region without recombining and are then swept across the base-collector junction into the collector region. A small percentage don't and these form the base current. the collector current is exponential in the base-emitter voltage:
iC=IS^e(vBE/VT)
To get a feel for this, consider this question: to double the collector current, how much would vBE need to increase?
For example, assuming the bias value is VBE=0.7V, increasing this voltage by a mere 17mV (an increase of just under 2.5%) will double the collector current.
According to the collector current equation, if we change the base-emitter voltage from its quiescent value by some small amount, the change in collector current is approximately:
ΔiC=(IC/VT)ΔvBE
As a typical example, let the quiescent collector current IC=1mA. At room temperature, VT=25mV.
Then, for these numbers, the collector current changes by 4% when the base-emitter voltage changes by 1mV.
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