Articles
<![CDATA[A new modified logistic growth model for empirical use ]]>
<![CDATA[Windarto, Windarto]]>;
<![CDATA[Eridani, Eridani]]>;
<![CDATA[Purwati, Utami Dyah]]>
<![CDATA[ Communication in Biomathematical Sciences Vol 1, No 2 (2018) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
Full PDF (263.141 KB)
|
DOI: 10.5614/cbms.2018.1.2.5
<![CDATA[Richards model, Gompertz model, and logistic model are widely used to describe growth model of a population. The Richards growth model is a modification of the logistic growth model. In this paper, we present a new modified logistic growth model. The proposed model was derived from a modification of the classical logistic differential equation. From the solution of the differential equation, we present a new mathematical growth model so called a WEP-modified logistic growth model for describing growth function of a living organism. We also extend the proposed model into couple WEP-modified logistic growth model. We further simulated and verified the proposed model by using chicken weight data cited from the literature. It was found that the proposed model gave more accurate predicted results compared to Richard, Gompertz, and logistic model. Therefore the proposed model could be used as an alternative model to describe individual growth.]]>
<![CDATA[Analisis Kestabilan Model Matematika Ko-infeksi Virus Influenza A dan Pneumokokus pada Sel Inang ]]>
<![CDATA[Abdul Faliq Anwar]]>;
<![CDATA[Windarto Windarto]]>;
<![CDATA[Cicik Alfiniyah]]>
<![CDATA[ Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 2 (2019) ]]>
Publisher : <![CDATA[Universitas Airlangga ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
Full PDF (780.616 KB)
|
DOI: 10.20473/conmatha.v1i2.17385
<![CDATA[Co-infection of influenza A virus and pneumococcus is caused by influenza A virus and pneumococcus bacteria which infected host cell at the same time. The purpose of this thesis is to analyze stability of equilibrium point on mathematical model within-host co-infection of influenza A and pneumococcus. Based on anlytical result of the model there are four quilibrium points, non endemic co-infection equilibrium (E0), endemic influenza A virus equilibrium (E1), endemic pneumococcus equilbrium (E2) and endemic co-infection equilibrium (E3). By Next Generation Matrix (NGM), we obtain two basic reproduction number, which are basic reproduction number for influenza A virus (R0v) and basic reproduction number for pneumococcus (R0b). Existence of equilibrium point and local stability of equilibrium point dependent on basic reproduction number. Non endemic co-infection equilibrium is locally asymtotically stable if R0v < 1 and R0b < 1; influenza A virus endemic equilibrium is locally asymtotically stable if R0v > 1 and R0b > 1; pneumococcus endemic equilibrium is locally asymtotically stable if R0v < 1 and R0b > 1. Meanwhile, the co-infection endemic equilibrium is locally asymtotically stable if R0v > 1 and R0b > 1. From the numerical simulation result, it was shown that increasing the number of influenza A virus and pneumococcus made the number of population cell infected by influenza A virus and pneumococcus (co-infection) also increased.]]>
<![CDATA[Analisis Kontrol Optimal Model Matematika Penyebaran Penyakit Mosaic pada Tanaman Jarak Pagar ]]>
<![CDATA[Adiluhung Setya Pambudi]]>;
<![CDATA[Fatmawati Fatmawati]]>;
<![CDATA[Windarto Windarto]]>
<![CDATA[ Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 2 (2019) ]]>
Publisher : <![CDATA[Universitas Airlangga ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
Full PDF (573.289 KB)
|
DOI: 10.20473/conmatha.v1i2.17386
<![CDATA[Mosaic disease is an infectious disease that attacks Jatropha curcas caused by Begomoviruses. Mosaic disease can be transmitted through the bite of a whitefly as a vector. In this paper, we studied a mathematical model of mosaic disease spreading of Jatropha curcas with awareness effect. We also studied the effect of prevention and extermination strategies as optimal control variables. Based on the results of the model analysis, we found two equilibriums namely the mosaic-free equilibrium and the endemic equilibrium. The stability of equilibriums and the existence of endemic equilibrium depend on basic reproduction number ( ). When , the spread of mosaic disease does not occur in the population, while when , the spread of mosaic disease occurs in the population. Furthermore, we determined existence of the optimal control variable by Pontryagin's Maximum Principle method. Simulation results show that prevention and extermination have a significant effect in eliminating mosaic disease.]]>
<![CDATA[Analisis dan Strategi Pengendalian Model Matematika Interaksi Sel Kanker Leukemia Mielositik Kronis dan Sel Imunitas ]]>
<![CDATA[Nanda Amalia Rahma]]>;
<![CDATA[Cicik Alfiniyah]]>;
<![CDATA[Windarto Windarto]]>
<![CDATA[ Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 2 (2020) ]]>
Publisher : <![CDATA[Universitas Airlangga ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.20473/conmatha.v2i2.23853
<![CDATA[Leukemia is a disease in the classification of cancer in the blood that is characterized by abnormal growth of blood cells in the bone marrow or lymphoid tissue, and generally occurs in leukocytes or white blood cells. White blood cells that look for types of pathogenic diseases that harm the human body and then damage it are the task of the immune system. This thesis analyzes the mathematical model of chronic myelocytic leukemia cancer cell interactions and immune cells to determine the rate of increase in the population of chronic myelocytic leukemia cancer cells to the effect of immune cells. Based on the analysis of the model obtained two equilibrium points namely the equilibrium point of the extinction of chronic myelocytic leukemia cancer cells (E0) and the equilibrium point of the coexistence of chronic myelocytic leukemia cancer cells (E1). The equilibrium point of extinction will be asymptotically stable, whereas the equilibrium point of coexistence tends to be asymptotically stable using phase fields with the help of MATLAB software. Numerical simulation results show that there is an increase in the number of chronic myelocytic leukemia cancer cell populations and a decrease in the number of vulnerable blood cell populations. When immune cells increase in population, chronic myelocytic leukemia in cancer cells decreases in population but is not significant.]]>
<![CDATA[Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate ]]>
<![CDATA[Dinda Ariska Putri]]>;
<![CDATA[Windarto Windarto]]>;
<![CDATA[Cicik Alfiniyah]]>
<![CDATA[ Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 1 (2021) ]]>
Publisher : <![CDATA[Universitas Airlangga ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.20473/conmatha.v3i1.26939
<![CDATA[Voter participation in general elections is an important aspect of a democratic state structure. Participation is determined by the level of public political awareness, if the level of public political awareness is low, voter participation tends to be passive (Abstinence). A mathematical model approach to voter participation in elections that has been modified to a saturated incidence rate is needed to predict voter participation in future elections. This thesis aims to analyze the stability of the equilibrium point and apply the optimal control variable in the form of an awareness campaign. In the model without control variables, we obtain two equilibriums, namely, the non-endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0), where R0=bL/(g+m)m. There is voter participation in elections when R0 < 1 and the absence of voter participation in elections when R0 > 1. We also analyze the sensitivity of parameters to determine which parameters are the most influential in this mathematical model. Furthermore, the application of control variables in the mathematical model of voter participation in elections with saturated incidence rate is determined through the Pontryagin Maximum Principle method. Numerical simulation results show that providing control variables in the form of awareness campaign it is quite effective in minimize the number of the voting population who abstained from election.]]>
<![CDATA[Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III ]]>
<![CDATA[Riris Nur Patria Putri]]>;
<![CDATA[Windarto Windarto]]>;
<![CDATA[Cicik Alfiniyah]]>
<![CDATA[ Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 2 (2021) ]]>
Publisher : <![CDATA[Universitas Airlangga ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.20473/conmatha.v3i2.30493
<![CDATA[Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.]]>
<![CDATA[A new modified logistic growth model for empirical use ]]>
<![CDATA[Windarto Windarto]]>;
<![CDATA[Eridani Eridani]]>;
<![CDATA[Utami Dyah Purwati]]>
<![CDATA[ Communication in Biomathematical Sciences Vol. 1 No. 2 (2018) ]]>
Publisher : <![CDATA[Indonesian Bio-Mathematical Society ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.5614/cbms.2018.1.2.5
<![CDATA[Richards model, Gompertz model, and logistic model are widely used to describe growth model of a population. The Richards growth model is a modification of the logistic growth model. In this paper, we present a new modified logistic growth model. The proposed model was derived from a modification of the classical logistic differential equation. From the solution of the differential equation, we present a new mathematical growth model so called a WEP-modified logistic growth model for describing growth function of a living organism. We also extend the proposed model into couple WEP-modified logistic growth model. We further simulated and verified the proposed model by using chicken weight data cited from the literature. It was found that the proposed model gave more accurate predicted results compared to Richard, Gompertz, and logistic model. Therefore the proposed model could be used as an alternative model to describe individual growth.]]>
<![CDATA[Pendekatan Numerik pada Model Penyebaran SARS dengan Method of Lines ]]>
<![CDATA[Patria Arif Bijaksana]]>;
<![CDATA[Windarto Windarto]]>;
<![CDATA[Fatmawati Fatmawati]]>
<![CDATA[ Limits: Journal of Mathematics and Its Applications Vol 15, No 1 (2018) ]]>
Publisher : <![CDATA[Institut Teknologi Sepuluh Nopember ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
Full PDF (430.006 KB)
|
DOI: 10.12962/limits.v15i1.3489
<![CDATA[Pada paper ini dikaji pendekatan numerik model matematika penyebaran SARS dengan adanya suku difusi. Suku difusi pada model tersebut mengilustrasikan penyebaran SARS berdasarkan lokasi. Solusi numerik dilakukan dengan menggunakan Method of Lines. Selanjutnya dibandingkan hasil simulasi numerik antara model penyebaran SARS tanpa suku difusi dan dengan adanya suku difusi. Hasil simulasi dari model penyebaran penyakit SARS tanpa suku difusi hanya menunjukkan terjadinya penyebaran SARS secara periodik waktu. Berdasarkan hasil simulasi pada model SARS dengan adanya suku difusi dapat diketahui bahwa penyebaran SARS dapat ditinjau dari titik awal penyebaran SARS secara spasial dan juga perodik waktu. Lebih lanjut, dari hasil simulasi menunjukkan bahwa semakin jauh dari pusat penyebaran SARS, laju penyebaran penyakit SARS akan semakin kecil]]>
<![CDATA[Analisis Kestabilan dan Kontrol Optimum pada Model Penyebaran Penyakit Influenza dengan Adanya Populasi Cross-Immune ]]>
<![CDATA[Bertha Aurellia Pamudya Fajar]]>;
<![CDATA[Miswanto]]>;
<![CDATA[Windarto]]>
<![CDATA[ Contemporary Mathematics and Applications (ConMathA) Vol. 4 No. 2 (2022) ]]>
Publisher : <![CDATA[Universitas Airlangga ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.20473/conmatha.v4i2.39168
<![CDATA[Influenza is a respiratory tract infection known as flu. Caused by an RNA virus from Orthomyxoviridae family. This thesis aims to analyze the stability of the equilibrium point in the mathematical model of influenza transmission with Cross-Immune population and applying optimal control variables in the form of prevention and treatment. In this mathematical model of influenza transmission with Cross-Immune population, we obtain two equilibriums namely, the non- endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0). The spread of influenza does not occur in the population when R0 < 1 and the spread of influenza persist in the population when R0 > 1. Furthermore, the problem of control variables in the mathematical model of influenza transmission is determined through the Pontryagin Maximum Principle method. The numerical simulation results show that treatment efforts are more effective in suppressing the spread of influenza disease than prevention efforts. However, giving control variables in the form of prevention and treatment at the same time is very effective in minimizing the number of human populations expose to and infected with influenza.]]>
<![CDATA[Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Leptospirosis dengan Saturated Incidence Rate ]]>
<![CDATA[Miswanto]]>;
<![CDATA[Nisrina Firsta Ammara]]>;
<![CDATA[Windarto]]>
<![CDATA[ Contemporary Mathematics and Applications (ConMathA) Vol. 5 No. 2 (2023) ]]>
Publisher : <![CDATA[Universitas Airlangga ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.20473/conmatha.v5i2.49379
<![CDATA[Leptospirosis is a disease caused by the bacteria Leptospira inchterohemorrhagiaea. Leptospirosis can attack humans and other animals, through rodents, especially rats. This research aims to analyze the stability of the equilibrium point in the mathematical model of the spread of Leptospirosis and apply optimal control variables in the form of prevention and treatment efforts. Based on the results of the mathematical model analysis of the spread of Leptospirosis, two equilibrium points were obtained, there are the non-endemic equilibrium point and the endemic equilibrium point. Local stability and the existence of an equilibrium point depend on the basic reproduction number . The non-endemic equilibrium point is local asymptotically stable if , while the endemic equilibrium point tends to be asymptotically stable if . Next, the problem of control variables in the model is determined using Pontryagin's Maximum Principle. Numerical simulation results show that providing control in the form of prevention efforts and treatment efforts simultaneously provides effective results in minimizing the population of individuals exposed to and infected by Leptospirosis at the cost of providing optimal control.]]>
