A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting
Caused by the bacterium Bacillus anthracis, anthrax is a serious zoonotic disease with a mortality rate of up to 60%. This disease naturally occurs in soil and commonly affects both domestic and wild animals worldwide. Humans are often infected with anthrax by consuming contaminated animal products....
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000233 |
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| author | Anita Triska Mona Zevika |
| author_facet | Anita Triska Mona Zevika |
| author_sort | Anita Triska |
| collection | DOAJ |
| description | Caused by the bacterium Bacillus anthracis, anthrax is a serious zoonotic disease with a mortality rate of up to 60%. This disease naturally occurs in soil and commonly affects both domestic and wild animals worldwide. Humans are often infected with anthrax by consuming contaminated animal products. This research focuses on the transmission of anthrax to herbivorous animals, particularly livestock, by examining animal harvesting practices and efforts to prevent its spread through vaccination. The SVICA deterministic model was developed to better understand the transmission of anthrax by categorizing the population into susceptible, vaccinated, and infected animals, as well as carcasses and anthrax spores. The basic reproduction number (R0) is calculated using the NGM method to determine the outbreak threshold in a population. Additionally, the model analyzes the local stability of two disease-free equilibrium points when R0<1 and shows the existence of an endemic equilibrium point when R0>1. Numerical exploration was conducted to examine the outbreak dynamics both generally and in specific cases. By varying the infection rate as a bifurcation parameter, it was found that when R0>1, there is a stable interval and an unstable interval for the endemic equilibrium point, separated by the Hopf bifurcation curve. When the endemic equilibrium is unstable, a limit cycle occurs. Two distinct limit cycle behaviors were observed with different limit cycle trends. One case exhibited a more even rate of change, while the other displayed a slow–fast limit cycle, indicating a situation where anthrax cases remain low for a time but then increase drastically. |
| format | Article |
| id | doaj-art-b758c19ab15d40ada4f908ce98efb9e8 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-b758c19ab15d40ada4f908ce98efb9e82025-02-07T04:48:26ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101095A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvestingAnita Triska0Mona Zevika1Department of Mathematics, Universitas Padjadjaran, Bandung, Indonesia; Corresponding author.Research Center for Applied Zoology, National Research and Innovation Agency, Bogor, IndonesiaCaused by the bacterium Bacillus anthracis, anthrax is a serious zoonotic disease with a mortality rate of up to 60%. This disease naturally occurs in soil and commonly affects both domestic and wild animals worldwide. Humans are often infected with anthrax by consuming contaminated animal products. This research focuses on the transmission of anthrax to herbivorous animals, particularly livestock, by examining animal harvesting practices and efforts to prevent its spread through vaccination. The SVICA deterministic model was developed to better understand the transmission of anthrax by categorizing the population into susceptible, vaccinated, and infected animals, as well as carcasses and anthrax spores. The basic reproduction number (R0) is calculated using the NGM method to determine the outbreak threshold in a population. Additionally, the model analyzes the local stability of two disease-free equilibrium points when R0<1 and shows the existence of an endemic equilibrium point when R0>1. Numerical exploration was conducted to examine the outbreak dynamics both generally and in specific cases. By varying the infection rate as a bifurcation parameter, it was found that when R0>1, there is a stable interval and an unstable interval for the endemic equilibrium point, separated by the Hopf bifurcation curve. When the endemic equilibrium is unstable, a limit cycle occurs. Two distinct limit cycle behaviors were observed with different limit cycle trends. One case exhibited a more even rate of change, while the other displayed a slow–fast limit cycle, indicating a situation where anthrax cases remain low for a time but then increase drastically.http://www.sciencedirect.com/science/article/pii/S2666818125000233AnthraxHopf bifurcationLimit cycleDeterministic modelHarvestingVaccination |
| spellingShingle | Anita Triska Mona Zevika A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting Partial Differential Equations in Applied Mathematics Anthrax Hopf bifurcation Limit cycle Deterministic model Harvesting Vaccination |
| title | A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting |
| title_full | A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting |
| title_fullStr | A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting |
| title_full_unstemmed | A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting |
| title_short | A Study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting |
| title_sort | study of the anthrax transmission model in herbivorous animals involving vaccination and harvesting |
| topic | Anthrax Hopf bifurcation Limit cycle Deterministic model Harvesting Vaccination |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000233 |
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