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A spatiotemporal model of meningococcal meningitis with direct and indirect transmission
Author(s) -
Zorom Malicki,
Andrianisa Harinaivo Anderson,
Dorville René,
Zongo Pascal
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6500
Subject(s) - ode , ordinary differential equation , basic reproduction number , mathematics , biological dispersal , transmission (telecommunications) , stability (learning theory) , partial differential equation , meningococcal meningitis , meningococcal disease , differential equation , bacteria , mathematical analysis , biology , computer science , medicine , environmental health , neisseria meningitidis , telecommunications , genetics , population , machine learning
We extend an ordinary differential equation (ODE) model for the meningococcal meningitis disease to a partial differential equation (PDE). This extension istwofold: (i) consideration of two modes of contamination, namely through a direct transmission (human to human) and an indirect transmission (via free‐living bacteria). (ii) consideration of the human movement and the dispersal of bacteria in a heterogeneous environment. Furthermore we show the existence of the solutions and define the basic reproduction numberR 0for the model. Additionally, the existence and the stability of both disease‐free and endemic equilibria were investigated. The sensitivity ofR 0and the endemic state with respect of the model parameters were studied. Numerical computations of the spreading bacteria are carried out to illustrate our mathematical results.