The Analysis of SEIRS-SEI Epidemic Models on Malaria with Regard to Human Recovery Rate

Abstract

This article discusses SEIRS-SEI epidemic models on malaria with regard to human recovery rate. SEIRS-SEI in this model is an abbreviation of the population class used in the model, i.e Susceptible, Exposed, Infected, and Recovered populations in humans and Susceptible, Exposed, and Infected populations in mosquito. These epidemic models belong to mathematical models which clarify a phenomenon of epidemic transmission of malaria by observing the human recovery rate after being infected and susceptible. Human population falls into four classes, namely susceptible humans, exposed humans, infected humans, and recovered humans. Meanwhile, mosquito population serving as vectors of the disease is divided into three classes, including susceptible mosquitoes, exposed mosquitoes, and infected mosquitoes. Such models are termed SEIRS-SEI epidemic models. Analytical discussion covers model formation, existence and stability of equilibrium points, as well as numerical simulation to find out the influence of human recovery rate on population dynamics of both species. The results show that the fixed point without disease ( ) is stable in condition ℛ 0 < 1and unstable in condition ℛ 0 > 1. The simulation results show that the given treatment has an influence on the dynamics of the human population and mosquitoes. If the human recovery rate from the infected state becomes susceptible to increased, then the number of infected populations of both species will decrease. As a result, the disease will not spread and within a certain time will disappear from the population.

Stability Analysis of Mathematical Model of Spread of Covid19 SEIRS Type with Constant Birth Rate

“…Modeling the Spread of Covid19 Infection in Kalimantan [5], An SIR epidemic model for Covid19 spread with fuzzy parameter: the case of Indonesia [6]. Several other studies related to mathematical modeling were conducted by [7]- [8].…”

“…In addition, the recovered -population is reduced because it moves to a susceptible population at a rate at which individuals recover to be revulnerable caused by the body's immune system declining. Based on the compartment diagram in Figure 1, a system of differential equations is obtained, namely: (8) with .…”

Model Epidemik Penyebaran Malaria

“…Beberapa penelitian sebelumnya yang membahas model penyebaran malaria dapat dilihat pada [1] [2]. Modifikasi model dilakukan dengan penambahan kelas terpapar (exposed) pada kedua populasi dengan mengacu pada [3].…”

Efektifitas Vaksinasi dan Pengasapan pada Model Epidemik Transmisi Penyakit Malaria

“…Dalam penelitian ini dibahas model transmisi penyakit malaria dari Laarabi et al, [6] dan Putri et al [8], dengan penambahan kelas terpapar (exposed) pada kedua populasi. Modifikasi serupa dapat dilihat pada Chitnis et al [3] dan Resmawan et al [9]. Hal ini diperlukan karena sporozoid yang dihasilkan dari gigitan nyamuk terinfeksi memerlukan masa inkubasi selama 9-14 hari untuk benar-benar menimbulkan penyakit (Bloland and Williams, [2]).…”