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All Journal SITEKIN: Jurnal Sains, Teknologi dan Industri Communication in Biomathematical Sciences KUBIK: Jurnal Publikasi Ilmiah Matematika
Mia Siti Khumaeroh
UIN Sunan Gunung Djati Bandung
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Industrial & Manufacturing Engineering Mathematics Social Sciences Other

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Biological and Mechanical Transmission Models of Dengue Fever Laura, Laura; Supriatna, Asep K.; Khumaeroh, Mia Siti; Anggriani, Nursanti
Communication in Biomathematical Sciences Vol 2, No 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1538.998 KB) | DOI: 10.5614/cbms.2019.2.1.2

Abstract

Dengue fever disease is caused by the dengue virus and transmitted primarily by the Aedes aegypti mosquitoes. There is no vaccine available to prevent transmission of the disease until recently which makes 30% of the worlds population is at risk of the disease. The Aedes aegypti mosquitoes are known as multiplebiters during their blood meal periods. There are two possible transmissions of the dengue virus from the mosquitoes to humans. First, infectious mosquitoes may transmit the virus through the bite to a susceptible human after the virus experiencing the extrinsic incubation period (EIP) in the body of the mosquitoes. Second, the transmission happens directly through the transfer of virus carried in the saliva of a mosquito to a susceptible human at the second bite without waiting for the EIP. The later is known as a mechanical transmission, which occurs when a susceptible mosquito bites an infectious human and almost at the same time it transmits the virus to a healthy human. Only a few literature consider this kind of dengue transmission. In this paper, we develop a mathematical model for dengue transmission by modifying the standard dengue transmission model with the presence of mechanical transmission. We show that the spreading behavior of the disease can be described by the basic reproduction number (BRN), R0. The disease will die out if R0 < 1, and it remains endemic if R0 > 1. The analysis shows that the ratio of the BRN in the presence and absence of the mechanical transmission increases as the mechanical transmission rate increases. There is also a significant change in the outbreak intensity especially when the mechanical transmission rate is greater than the biological transmission rate.
A Dynamical Model of ’Invisible Wall’ in Mosquito Control Mia Siti Khumaeroh; Edy Soewono; Nuning Nuraini
Communication in Biomathematical Sciences Vol. 1 No. 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2018.1.2.2

Abstract

A concept of an ’invisible wall’ is used here as a control mechanism to separate the human population from mosquitoes in the hope that mosquitoes gradually change their preference to other blood resources. Although mosquitoes carry inherent traits in host preference, in a situation in which regular blood resource is less available, and there are abundant other blood resources, mosquitoes may adapt to the existing new blood resource. Here we construct a model of mosquitoes preference alteration involving anthropophilic, opportunistic, and zoophilic, based on the application of repellent clothing usage and the effects of fumigation. The coexistence equilibrium is shown to be stable when the rate of mosquito ovulation, which is successfully hatching into larvae, is greater than the total of mosquito natural death rate and mosquito death rate due to fumigation. Numerical simulation is performed after the reduction of unobservable parameters is done with Human Blood Index (HBI) data. Global sensitivity analysis is then performed to determine the parameters that provide the dominant alteration effect on the mosquito population. The simulation results show that a proper selection of the fumigation rate and repellent clothing rate should be carefully done in order to reduce the mosquito population as well as to increase the zoophilic ratio.
Biological and Mechanical Transmission Models of Dengue Fever Laura Laura; Asep K. Supriatna; Mia Siti Khumaeroh; Nursanti Anggriani
Communication in Biomathematical Sciences Vol. 2 No. 1 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2019.2.1.2

Abstract

Dengue fever disease is caused by the dengue virus and transmitted primarily by the Aedes aegypti mosquitoes. There is no vaccine available to prevent transmission of the disease until recently which makes 30% of the worlds population is at risk of the disease. The Aedes aegypti mosquitoes are known as multiplebiters during their blood meal periods. There are two possible transmissions of the dengue virus from the mosquitoes to humans. First, infectious mosquitoes may transmit the virus through the bite to a susceptible human after the virus experiencing the extrinsic incubation period (EIP) in the body of the mosquitoes. Second, the transmission happens directly through the transfer of virus carried in the saliva of a mosquito to a susceptible human at the second bite without waiting for the EIP. The later is known as a mechanical transmission, which occurs when a susceptible mosquito bites an infectious human and almost at the same time it transmits the virus to a healthy human. Only a few literature consider this kind of dengue transmission. In this paper, we develop a mathematical model for dengue transmission by modifying the standard dengue transmission model with the presence of mechanical transmission. We show that the spreading behavior of the disease can be described by the basic reproduction number (BRN), R0. The disease will die out if R0 < 1, and it remains endemic if R0 > 1. The analysis shows that the ratio of the BRN in the presence and absence of the mechanical transmission increases as the mechanical transmission rate increases. There is also a significant change in the outbreak intensity especially when the mechanical transmission rate is greater than the biological transmission rate.
Analisis Sensitivitas dan Kestabilan Global Model Pengendalian Tuberkulosis dengan Vaksinasi, Latensi dan Perawatan Infeksi Della Isna Amatillah; Fadilah Ilahi; Mia Siti Khumaeroh
KUBIK Vol 6, No 2 (2021): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v6i2.14938

Abstract

Tuberculosis is an infectious disease caused by the bacterium Mycobacterium tuberculosis which attacks the lungs. Tuberculosis or TB is one of the diseases with the highest mortality rate in the world. In this article, we will examine the sensitivity and global stability analysis of the tuberculosis control model with vaccination, latency and infection treatment. In this model, the population is divided into 5 compartments, namely the immunized population (M), susceptible population (S), infected population with latent TB (L), infected population with active TB (I) and the recovered population (R).  The equilibrium point, local and global stability, basic reproduction number R0 is analyzed along with sensitivity analysis to see the effect of parameter values on the basic reproduction number R0. From the analysis and simulation result, it is found that there are two parameters that have the most influence on the spread of tuberculosis, namely the recovery rate of latent TB and the infection rate of active TB. If the recovery rate of latent TB is higher than the infection rate of active TB infection, then the disease will gradually disappear from the population, whereas if the recovery rate of latent TB is lower than the infection rate of active TB, the disease will spread within the population.
Model Matematika untuk Penyakit Infeksi Cacing Parasit pada Kuda Elvi Syukrina Erianto; Mia Siti Khumaeroh
SITEKIN: Jurnal Sains, Teknologi dan Industri Vol 20, No 1 (2022): Desember 2022
Publisher : Fakultas Sains dan Teknologi Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/sitekin.v20i1.20415

Abstract

Pada dasarnya, kuda merupakan inang bagi beberapa cacing parasit seperti Helminth. Spesies cacing parasit ini, contohnya Parascaris equorum, biasanya ditemukan dalam usus kecil kuda. Pada kasus infeksi yang parah, parasit ini dapat menyebabkan inefisiensi, kehilangan energi, dan terkadang kolik pada kuda. Dalam artikel ini, dibangun model matematika penyebaran penyakit infeksi cacing pada kuda, dengan mempertimbangkan siklus hidup cacing pada kuda dan di lapangan. Populasi kuda dibagi menjadi kompartemen kuda sehat , kuda ekspos, dan kuda terinfeksi Sementara kompartemen cacing terbagi menjadi telur  dan larva . Ada dua titik kesetimbangan yang akan dibahas yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Rasio reproduksi dasar diperoleh dan simulasi numerik ditampilkan.
Co-Authors Aldri Frinaldi Asep K. Supriatna Della Isna Amatillah Edy Soewono Elvi Syukrina Erianto Fadilah Ilahi Laura Laura Laura, Laura Nuning Nuraini Nursanti Anggriani Supriatna, Asep K.