Improvement of disease dynamics monitoring through systematic screening and patchy structure: application to Neissera Meningitidis

Abstract

This work is concerned with the estimation a Neissera meningitidis dynamics according to a Susceptible-Carrier-Infectious-Recovered-Hospitalized (SCIRH) model extending a recent SCIR model studied in the literature. The extension consists in taking into consideration the fact that infectious individuals are not systematically reported and followed by hospitals. Indeed, for different reasons encountered especially in sub-Saharan Africa, people may experience difficulties to go to the hospital (for example disadvantaged status, cultural habits and unavailability of hospital centers in the neighborhood). We also consider the relaxing hypothesis that the size of the total population is unknown and only the size in compartment H is known by following patients. Based on a theoretical result stated and proved first, we propose an exponentially convergent observer for the SCIRH model. We additionally establish that the convergence of the above observer can be substantially improved if systematic screening campaigns and a patchy structure are adopted. Precisely, a new observer is constructed using new stability criteria that we state and prove for the class n-Metzler matrices introduced in the current work. For each of the two observers given here, numerical simulations are carried out in order to concretely appreciate their convergence. As theoretically announced, both of the observers converge exponentially with the respective rates 0.0146298 and 0.5011. Hence, the improvements due to screening and patchy structure multiply the initial exponential convergence rate by 34.252006.

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Fig. 1
Fig. 2

Notes

  1. 1.

    See the references in Briat (2017) for example.

  2. 2.

    Notice that a M-matrix is just the opposite of a Metzler matrix.

  3. 3.

    See the book Berman and Plemmons (1994); Luenberger (1979).

  4. 4.

    See the book La Salle (1976).

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Acknowledgements

The author is very grateful to the anonymous editors and reviewers whose recommendations have substantially increased the quality of this work.

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Correspondence to David Jaurès Fotsa-Mbogne.

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Communicated by Valeria Neves Domingos Cavalcanti.

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Fotsa-Mbogne, D.J. Improvement of disease dynamics monitoring through systematic screening and patchy structure: application to Neissera Meningitidis. Comp. Appl. Math. 40, 32 (2021). https://doi.org/10.1007/s40314-021-01417-6

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Keywords

  • Neissera Meningitidis
  • Compartmental modeling
  • State estimation
  • Nonlinear observer
  • Metzler matrices

Mathematics Subject Classification

  • 92C60
  • 92D30
  • 93B07
  • 93C15
  • 93C41