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Global dynamics for mathematical model of Echinococcus multilocularis in rodents and red foxes
Author(s) -
Hassan Adamu Shitu,
Munganga Justin M. W.
Publication year - 2020
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.6327
Subject(s) - mathematics , basic reproduction number , echinococcus multilocularis , alveolar echinococcosis , statistical physics , statistics , econometrics , biology , mathematical economics , echinococcosis , zoology , physics , population , demography , sociology
A deterministic model for transmission of Echinococcus multilocularis (EM) , a parasitic disease responsible for human alveolar echinococcosis, is formulated and analyzed rigorously. The model consists of two hosts, with three compartments each, and concentration of the parasites from environment as sources of infection. The model takes into account a predator‐prey relationship between the major hosts and obtained a threshold value for their existence. Systematic derivation of basic reproduction number,R 0 , is provided. Thorough qualitative analysis of the model reveals that it has a local and global asymptotic stable disease‐free equilibrium whenR 0 < 1 ; thus, ( EM ) will die out in the populations. However, whenR 0exceeds unity, the model exhibits a unique endemic equilibrium, which is globally asymptotic stable; hence, disease will persist. The elasticity indices and partial rank correlation coefficients of the basic reproduction number and cumulative new cases of the two hosts with respect to parameter values are computed. Sensitivity analyses identified key parameters that are the most sensitive and can be used for control strategies in reducingR 0below unity. Numerical simulations are used to verify theoretical results and quantify prevalence of the disease in host populations.