A MODEL OF THE DYNAMIC OF TRANSMISSION OF MALARIA, INTEGRATING SEIRS,SEIS,SIRS AND SIS ORGANIZATION IN THE HOST-POPULATION

J. C Kamgang; S. Y Tchoumi

doi:10.11948/2015053

2015 Volume 5 Issue 4

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J. C Kamgang, S. Y Tchoumi. A MODEL OF THE DYNAMIC OF TRANSMISSION OF MALARIA, INTEGRATING SEIRS,SEIS,SIRS AND SIS ORGANIZATION IN THE HOST-POPULATION[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 688-703. doi: 10.11948/2015053

Citation:

J. C Kamgang, S. Y Tchoumi. A MODEL OF THE DYNAMIC OF TRANSMISSION OF MALARIA, INTEGRATING SEIRS,SEIS,SIRS AND SIS ORGANIZATION IN THE HOST-POPULATION[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 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

J. C Kamgang¹,
S. Y Tchoumi²

1 Department of Mathematics and Computer Sciences ENSAI-University of N'Gaoundéré, P. O. Box 455 N'Gaoundéré(Cameroon);
2 Department of Mathematics and Computer Sciences, Faculty of Science University of N'Gaoundéré, P. O. Box 454, N'Gaoundéré(Cameroon

Abstract

Abstract

In this paper, we propose and analyse a model of dynamics transmission of malaria, incorporating varying degrees p of susceptible and π of infectious that makes the dynamic of the overall host population integrate SEIRS,SEIS,SIRS and SIS at the same time. For this model we compute a new threshold number ζ and establish the global asymptotic stability of the disease-free equilibrium when R₀ < ζ < 1. If ζ < R₀ < 1, the system admits a unique endemic equilibrium (EE) and if R₀ > 1 depending on case the system admits one or two endemic equilibrium. Numerical simulations are presented for different value of R₀, based on data collected in the literature. Finally, the impact of parameters p and π of system dynamics are investigated.
- Epidemiological model /
- malaria /
- basic reproduction number /
- global asymptotic stability /
- non-standard finite difference scheme(NFDS) /
- simulation
MSC: 34C60;34D20;34D23;92D30

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References

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