Article Contents
Article Contents

# Modeling the transmission of dengue fever with limited medical resources and self-protection

• * Corresponding author
The work is supported by the NSFC of China (Grant No. 11371311) and Graduate Research and Innovation Projects of Jiangsu Province (Grant No. KYZZ16−0489)
• To capture the impacts of limited medical resources and self-protection on the transmission of dengue fever, we formulate an SIS v.s. SI dengue model with the nonlinear recovery rate and contact transmission rate. The spatial heterogeneity of environment is also taken into consideration. With the aid of the relevant eigenvalue problem, we explore some properties of the basic reproduction number, and show that it still plays its "traditional" role in determining the stability of equilibria, that is, the extinction and persistence of dengue fever. Moreover, we consider a special diffusive pattern in which there is only human diffusion, but no mosquitoes diffusion, then present the explicit expression of the basic reproduction number and exhibit the corresponding transmission dynamics. This paper ends up with some numerical simulations and epidemiological explanations, which confirm our analytical findings.

Mathematics Subject Classification: Primary: 35K20, 35B40; Secondary: 92D30.

 Citation:

• Figure 1.  $p = 10$ and $h = 1.65$. Graphs (a) and (b) show that the solution $(I_H, I_V)$ decays to zero, which means the dengue virus is vanishing.

Figure 2.  $p = 5$ and $h = 1.65$. From graphs (a) and (b), we can see that the solution $(I_H, I_V)$ keeps positive and stabilizes to an equilibrium, which is globally asymptotically stable, that is to say the dengue virus is spreading.

Figure 3.  $p = 10$ and $h = 0.7$. One can observe the long-time behavior of the solution $(I_H, I_V)$, where the dengue virus $I_H$ and $I_V$ don't vanish, and spread gradually.

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