| Citation: |
Rehana Naz, Gangwei Wang, Saba Irum. THE CLOSED-FORM SOLUTIONS OF A DIFFUSIVE SUSCEPTIBLE-INFECTIOUS-SUSCEPTIBLE EPIDEMIC MODEL[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 574-586. doi: 10.11948/20240175
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THE CLOSED-FORM SOLUTIONS OF A DIFFUSIVE SUSCEPTIBLE-INFECTIOUS-SUSCEPTIBLE EPIDEMIC MODEL
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Abstract
We establish the closed-form solutions of the Susceptible-Infectious-Susceptible (SIS) epidemic model with diffusion using Lie point symmetries. The model admits a four-dimensional Lie algebra. We use different combinations of Lie symmetries to construct the closed-form solutions. We consider appropriate initial and boundary conditions to explore the biological relevance of these closed-form solutions. We utilize the closed-form solutions to study the transmission dynamics of an influenza outbreak with Gaussian initial distributions. We plot graphs for the susceptible and infected populations. We consider the lower diffusion coefficient and higher diffusion coefficient cases to analyze the transmission dynamics of the influenza outbreak.
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Keywords:
- Diffusive SIS model /
- Lie symmetries /
- closed-form solutions
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References
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Rehana Naz, Gangwei Wang, Saba Irum. THE CLOSED-FORM SOLUTIONS OF A DIFFUSIVE SUSCEPTIBLE-INFECTIOUS-SUSCEPTIBLE EPIDEMIC MODEL[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 574-586. doi: 10.11948/20240175
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Figure 1.
The graphs of initial distribution of susceptible and infected individuals across the domain for different values of
$ \lambda=\frac{c_4 }{2c_2} $ $ 0\leq x\leq 10 $ -
Figure 2.
Graphs of
$ S(x) $ $ I(x) $ $ \delta=0.02 $ $ \delta=0.1 $ $ c_2=10 $ $ c_4=1 $ $ \beta=0.4 $ $ \gamma=0.2 $ $ S_0=10^5-200 $ $ I_0=200 $ $ 0\leq x\leq 10 $ -
Figure 3.
Graphs of
$ S(t) $ $ I(t) $ $ \delta=0.02 $ $ \delta=0.1 $ $ c_2=10 $ $ c_4=1 $ $ \beta=0.4 $ $ \gamma=0.2 $ $ S_0=10^5-200 $ $ I_0=200 $ $ 0\leq t\leq 200 $ -
Figure 4.
Surface plots of
$ S $ $ I $ $ \delta=0.02 $ $ \delta=0.1 $ $ c_2=10 $ $ c_4=1 $ $ \beta=0.4 $ $ \gamma=0.2 $ $ S_0=10^5-200 $ $ I_0=200 $ $ 0\leq t\leq 200 $ $ 0\leq x\leq 10 $