a The frequency of a certain gene in a parasite population u

a) The frequency of a certain gene in a parasite population undergoes sinusodial cycles as a result of coevolution with its host. it reaches a maximum frequency of 80% and a minimum of 20%, with a complete cycle taking 3 years. Find a function that describes the gene frequency dynamics over time(measured in years) assuming that it starts at a frequency of 50% at time t=0.

b) Cyclic Neutropenia is a blood disorder in humans characterized by periodic fluctuations in the density of a certain kind of blood cell called neutrophils. The density of neutrophils reaches highs of around 2000 cells/ uL of blood and lows near zero. The period of fluctuation is approximately 3 weeks.Model the temporal dynamics of neutrophils in days, assuming that the density is the highest on day 0.

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Solution

a) Assuming frequency of a gene is 50% at time =0, and it undergoes 80% maximum increase in frequency and then it reduces to 20% in 3 years and in a cyclic manner (Sinusodial cycle). The function describing gene frequency is sine and cosine functions having period of 3 years (Sin(x+2pi)=Sinx/ Cos (x+2pi)=cosx) where 20%<sin x <80%

b) The density of neutrophils reaches highs of around 2000 cells/ uL of blood and lows near zero in a periodic manner. when cells lowers to zero i.e. Sin x =0, x=n*pi where n =2 in weeks. Temporal dynamics of neutrophils is (Sin(x+2pi)=Sinx/ Cos (x+2pi)=cosx)