| Volume 5, Number 4, 2015, Pages 688-703 DOI：10.11948/2015053 |
| A model of the dynamic of transmission of malaria, integrating SEIRS, SEIS, SIRS and SIS organization in the host-population |
| S. Y. Tchoumi,J. C. Kamgang |
| Keywords:Epidemiological model, malaria, basic reproduction number, global asymptotic stability, non-standard |
| Abstract: |
| In this paper, we propose and analyse a model of dynamics trans-mission of malaria, incorporating varying degrees p of susceptible and ofinfectious that makes the dynamic of the overall host population integrateSEIRS, SEIS, SIRS and SIS at the same time. For this model we compute anew threshold number and establish the global asymptotic stability of thedisease-free equilibrium when R0 < < 1. If < R0 < 1, the system admits aunique endemic equilibrium (EE) and if R0 > 1 depending on case the systemadmits one or two endemic equilibrium. Numerical simulations are presentedfor dierent value of R0, based on data collected in the literature. Finally,the impact of parameters p and of system dynamics are investigated. |
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