SEIR Epidemic Model

Epidemic Model For Ebola

Stochastic Model

Mastik Kumar

153070031

Department of Electrical Engineering

Indian Institute of Technology, Bombay

Mumbai, India [e-mail] , [e-mail]

Abstract— Considering the huge global influence of Ebola, its an urgent task to think out an approach to eradicate its spread. In this paper, I built a SEIR model which succeeds in optimizing the eradication of Ebola. Firstly, I establish the Rudimentary epidemic model (without any intervention) and model fitting validation method to solve the differential equations and then establish An epidemic model with intervention. In Intervention model, there are three types of interventions model which is composed of three sub-models: Quarantine

Large amounts of researches have been made both in epidemic model and delivery model. For example, Kermack and McKendrick proposed an epidemic model called the SIR Epidemic model. Also, there is a delivery model called Pulse Vaccination Strategy which is proposed by Boris Shulgin. In spite of the existing studies in this field, they both have their own disadvantages. SIR model or SEIR model’s classification of people is not accurate enough in Ebola’s spread, while the pulse vaccination strategy is most commonly used during measles and polio epidemics. Therefore, I spared great efforts to establish a creative mathematical model which is reasonable and reliable enough to help with the eradication of Ebola. Firstly, this paper establish the RISK model which is modified by the classic SIR model. This model helps us to predict the future tendency of the diseases spread and examine the effectiveness of the delivery strategy. Then, this paper establish the delivery model to make sure our delivery strategy of medicine. The delivery model is divided into three sub-models: the production model, the transportation model and the distribution model. Through analyzing and calculating the elements in the sub-models, we give out a reasonable delivery strategy. Finally, this

Kermack and McKendrick Equation :

dS/dt=-βSI/N dE/dt=βSI/N-δE dI/dt=δE-γI dR/dt=γI N(t)=S(t)+E(t)+I(t)+R(t)

Here, I have β=pc ; where p denotes the probability of successful getting infected when coming into contact with an infected person and c is the per-capita contact rate.

The individuals in the latent stage will eventually show the symptoms of the disease and enter into the infectious stage. This is denoted as δE, where δ is the per-capita infectious rate. In that case, 1/δ becomes the average time for a latent individual to become infectious.

The death rate is denoted by γI, where γ is the per-capita death rate. Here, although recoveries do occur, we will not return these individuals to the susceptible class again (actually even if we do, the number of recovered individuals reported so far is extremely small, so it really doesn’t matter here).

The method structure can be described in a flow chart as below, note that the arrows indicate the possible transitions, and the parameters that govern them.

Flow