Template:NYMU-2015project-drylab-Epidemic

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Project

Model

Epidemic

P. infestans is an oligate parasite, which means it can’t complete its life cycle without exploiting potato. However, if a potato is infected by P. infestans, the disease will spread through the potato farm within 20 days.

In this model, we try to show the difference between planting the potato we engineered and planting potato that is susceptible or moderately resistant to potato late blight. Traditionally, SEIR model will be the perfect model to characterize epidemiology. However, we made some changes to the assumption of the traditional SEIR model so that the model can reflect the reality of potato late blight epidemiology much better.

Symbol	Meaning
Suspected	The potato that is slightly or moderately resistant to P.infestans
Exposed	Potatoes that are infected by a low amount of P.infestans, but they are still curable andwill not spread the disaese
Infected	Potatoes that are infected by a large amount of P.infestans. Potatoes infected will spread the disease and jeopardize the whole potato farm
Immunized	Potatoes that has been transformed by us and is resistant against P.infestans

According to our assumptions, we developed a set of ordinary differential equations that can characterize the epidemic of potato late blight.

Parameters

γ	transmission rate(1/days)	0.25
α	Promoter activation rate(1/days)	1.0
SEIR MODEL	ε	Latent rate(1/days)	0.2	British Columbia Ministry of Agriculture[3]
(COEFFICIENTS)	μ	Infection rate(1/days)	0.2
k	Rate of resistance to late blight	0.75	External Lipid PI3P Mediates Entry of Eukaryotic Pathogen Effectors into Plant and Animal Host Cells[2]
beta	Daeth rate of normal potato(1/days)	1/365
S	The amount of all potatoes	X(1)
E	The amount of suspected individual	X(2)	Global analysis of an SEIR model with varying population size and vaccination
SEIR MODEL	I	The amount of infected individual	X(3)	[1]
(VARIABLE)	R	The amount of potato that survive	X(4)
V	The amount of potato being immunized	X(5)

Result

As we can see from the model,with our genetically modified potatoes can prevent 80% of the potatoes from being infected, while only 20% of the moderately resistant potatoes can survive during the epidemic of potato late blight. Also as we can see in the graphs above, the survival rate do fit our sassumption the the potatoes under the destruction of late blight only end in two consequences----death(once the potatoes exposed to small amount of p.infestans are seriously infected ) or survive (once the “exposed potato” truned into “immunized potato”). This graphs not only show that our potatoes might be effective in fighting potato late blight in the real world but also show that potato late blight is a disease that needs to be take care of seriously and a impeccible system is necessary to fight against the disease.

Conclusion

As we can see from the model,with our genetically modified potatoes can prevent 80% of the potatoes from being infected, while only 20% of the moderately resistant potatoes can survive during the epidemic of potato late blight. Also as we can see in the graphs above, the survival rate do fit our sassumption the the potatoes under the destruction of late blight only end in two consequences----death(once the potatoes exposed to small amount of p.infestans are seriously infected ) or survive (once the “exposed potato” truned into “immunized potato”). This graphs not only show that our potatoes might be effective in fighting potato late blight in the real world but also show that potato late blight is a disease that needs to be take care of seriously and a impeccible system is necessary to fight against the disease.

Reference

1. Chengjun Suna, Ying-Hen Hsiehc. “Global analysis of an SEIR model with varying population size and vaccination” doi:10.1016/j.apm.2009.12.005
2. Kale SD1, Gu B, Capelluto DG, Dou D, Feldman E, Rumore A, Arredondo FD, Hanlon R, Fudal I, Rouxel T, Lawrence CB, Shan W, Tyler BM. “External Lipid PI3P Mediates Entry of Eukaryotic Pathogen Effector into Plant and Animal Host Cells” Cell. 2010 Sep 17;142(6):981-3.
3. British Columbia Ministry of Agriculture