archives@tulane.edu / We extend the conventional models in mathematical epidemiology to account for more practical (yet complicated) situations in infectious disease transmissions, such as behavior change, risk level differentiation and infectiousness as a function of time since infection. We allow the transmission rate and recovery rate to vary as functions of time since infection. We present the derivation of the integral differential equation model and analyze the associated analytical and long-time solutions. We prove the well-posedness of an initial boundary value problem for the model. We also derive the threshold quantities for the epidemic to grow. We then extend the approach for the vector-borne infectious disease models. We compare several risk distribution functions due to geographic reasons. We construct the behavior change factor for the host population to account for different levels of infectiousness due to behavior distinction and behavior change. We establish the well-posedness of an initial boundary value problem of the new model. Sensitivity analysis shows that different risk distribution functions that are designed to adjust for spatial and geographic reasons have a large impact on the solution. / 1 / Li Guan
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_110765 |
| Date | 31 December 2019 |
| Contributors | Guan, Li (author), Hyman, James (Thesis advisor), School of Science & Engineering Mathematics (Degree granting institution) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | electronic, pages: 155 |
| Rights | No embargo, Copyright is in accordance with U.S. Copyright law. |
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