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Mathematical Model for MRSA Nasal Carriage

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Abstract

An interesting biological phenomenon that is a factor for the spread of antibiotic-resistant strains, such as MRSA, is human nasal carriage. Here, we evaluate several biological hypotheses for this problem in an effort to better understand and narrow the scope of the dominant factors that allow these bacteria to persist in otherwise healthy individuals. First, we set up and analyze a simple PDE model created to generally mimic the interactions of the microbes and nasal immune response. This includes looking at different types of diffusion and chemotaxis terms as well as different boundary conditions. Then, using sensitivity analysis, we walk through several biological hypotheses and compare to the model’s results looking for persistent infection scenarios indicated by the model’s bacteria component surviving over time.

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, 208 Love Building, 1017 Academic Way, Tallahassee, FL, 32306, USA

    Angela M. Jarrett, N. G. Cogan & M. Y. Hussaini

Authors
  1. Angela M. Jarrett
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  2. N. G. Cogan
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  3. M. Y. Hussaini
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Correspondence to Angela M. Jarrett.

Appendix

Appendix

See Tables 2, 3, 4, 5 and Figs. 14, 15.

Table 2 Parameter descriptions and values: The model variables quantify the response of each component rather than give a quantitative count due to the fact that several of the components in the biological system are combined
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Table 3 PRCC results for constant diffusion
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Table 4 PRCC results for non-constant diffusion
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Table 5 PRCC results for non-constant diffusion over space
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Fig. 14
figure 14

Results for the full model testing changes in the mucus parameters \(\textit{DB}\), \(\textit{DN}\), and \(\xi \). When \(\textit{DB}\) and \(\textit{DN}\) are decreased, the infection is able to remain for a longer period of time, but \(\textit{DB}\) has a far more significant effect. When \(\xi \) is increased, it also gives the infection an advantage to survive. a B results for decreased \(\textit{DB}=0.3\). b N results for decreased \(\textit{DB}=0.3\). c B results for decreased \(\textit{DN}=0.1\). d N results for decreased \(\textit{DN}=0.1\). e B results for increased \(\xi =0.22\). f N results for increased \(\xi =0.22\). g B results for increased \(\xi =0.4\). h N results for increased \(\xi =0.4\) (Color figure online)

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Fig. 15
figure 15

Graphs are the PRCC results from the tables above where the black dashed lines represent the value 0.25 for possible sensitivity and the red dashed lines represent the cutoff for most significance (value 0.45). a PRCC results for constant diffusion and constant N boundary condition. b PRCC results for constant diffusion and non-constant N boundary condition. c PRCC results for non-constant diffusion in time and constant N boundary condition. d PRCC results for non-constant diffusion in time and non-constant N boundary condition. e PRCC results for non-constant diffusion in time and space and constant N boundary condition. f PRCC results for non-constant diffusion in time and space and non-constant N boundary condition (Color figure online)

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Jarrett, A.M., Cogan, N.G. & Hussaini, M.Y. Mathematical Model for MRSA Nasal Carriage. Bull Math Biol 77, 1787–1812 (2015). https://doi.org/10.1007/s11538-015-0104-6

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