Preprint Article Version 1 This version is not peer-reviewed

Stability Analysis and Semi-analytic Solution to a SEIR-SEI Malaria Transmission Model Using HE’s Variational Iteration Method

Version 1 : Received: 30 May 2020 / Approved: 31 May 2020 / Online: 31 May 2020 (17:39:41 CEST)

How to cite: Akinfe, K.T.; Loyinmi, A.C. Stability Analysis and Semi-analytic Solution to a SEIR-SEI Malaria Transmission Model Using HE’s Variational Iteration Method . Preprints 2020, 2020050484 (doi: 10.20944/preprints202005.0484.v1). Akinfe, K.T.; Loyinmi, A.C. Stability Analysis and Semi-analytic Solution to a SEIR-SEI Malaria Transmission Model Using HE’s Variational Iteration Method . Preprints 2020, 2020050484 (doi: 10.20944/preprints202005.0484.v1).

Abstract

We have considered a SEIR-SEI Vector-host mathematical model which captures malaria transmission dynamics, described and built on 7-dimensional nonlinear ordinary differential equations. We compute the basic reproduction number of the model; examine the positivity and boundedness of the model compartments in a region using well established methods viz: Cauchy’s differential theorem, Birkhoff & Rota’s theorem which verifies and reveals the well-posedness, and carrying capacity of the model respectively, the existence of the Disease-Free (DFE) and Endemic (EDE) equilibrium points were determined and examined. Using the Gaussian elimination method and the Routh-hurwitz criterion, we convey stability analyses at DFE and EDE points which indicates that the DFE (malaria-free) and the EDE (epidemic outbreak) point occurs when the basic reproduction number is less than unity (one) and greater than unity (one) respectively. We obtain a solution to the model using the Variational iteration method (VIM) (an unprecedented method) to each population compartments and verify the efficacy, reliability and validity of the proposed method by comparing the respective solutions via tables and combined plots with the computer in-built Runge-kutta-Felhberg of fourth-fifths order (RKF-45). We illustrate the combined plot profiles of each compartment in the model, showing the dynamic behavior of these compartments; then we speculate that VIM is efficient and capable to conduct analysis on Malaria models and other epidemiological models.

Subject Areas

SEIR-SEI; Basic Reproduction number; Disease-Free equilibrium point (DFE); Endemic equilibrium point; Stability; Variational iteration method (VIM); Runge-Kutta-Felhberg (RKF-45)

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.