Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment
In this paper we present a mathematical model for the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by considering antibiotic treatment and vaccination. The model is comprised of susceptible, vaccinated, exposed, infectious, persistently infected, and recovered compartments. We a...
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Wiley
2019-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/2490313 |
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| author | Achamyelesh Amare Aligaz Justin Manango W. Munganga |
| author_facet | Achamyelesh Amare Aligaz Justin Manango W. Munganga |
| author_sort | Achamyelesh Amare Aligaz |
| collection | DOAJ |
| description | In this paper we present a mathematical model for the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by considering antibiotic treatment and vaccination. The model is comprised of susceptible, vaccinated, exposed, infectious, persistently infected, and recovered compartments. We analyse the model by deriving a formula for the control reproduction number Rc and prove that, for Rc<1, the disease free equilibrium is globally asymptotically stable; thus CBPP dies out, whereas for Rc>1, the unique endemic equilibrium is globally asymptotically stable and hence the disease persists. Thus, Rc=1 acts as a sharp threshold between the disease dying out or causing an epidemic. As a result, the threshold of antibiotic treatment is αt⁎=0.1049. Thus, without using vaccination, more than 85.45% of the infectious cattle should receive antibiotic treatment or the period of infection should be reduced to less than 8.15 days to control the disease. Similarly, the threshold of vaccination is ρ⁎=0.0084. Therefore, we have to vaccinate at least 80% of susceptible cattle in less than 49.5 days, to control the disease. Using both vaccination and antibiotic treatment, the threshold value of vaccination depends on the rate of antibiotic treatment, αt, and is denoted by ραt. Hence, if 50% of infectious cattle receive antibiotic treatment, then at least 50% of susceptible cattle should get vaccination in less than 73.8 days in order to control the disease. |
| format | Article |
| id | doaj-art-a9a3dd1bc5ec4dccae556d574f08d8ff |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a9a3dd1bc5ec4dccae556d574f08d8ff2025-08-20T02:20:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422019-01-01201910.1155/2019/24903132490313Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic TreatmentAchamyelesh Amare Aligaz0Justin Manango W. Munganga1Department of Mathematical Sciences, University of South Africa, South AfricaDepartment of Mathematical Sciences, University of South Africa, South AfricaIn this paper we present a mathematical model for the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by considering antibiotic treatment and vaccination. The model is comprised of susceptible, vaccinated, exposed, infectious, persistently infected, and recovered compartments. We analyse the model by deriving a formula for the control reproduction number Rc and prove that, for Rc<1, the disease free equilibrium is globally asymptotically stable; thus CBPP dies out, whereas for Rc>1, the unique endemic equilibrium is globally asymptotically stable and hence the disease persists. Thus, Rc=1 acts as a sharp threshold between the disease dying out or causing an epidemic. As a result, the threshold of antibiotic treatment is αt⁎=0.1049. Thus, without using vaccination, more than 85.45% of the infectious cattle should receive antibiotic treatment or the period of infection should be reduced to less than 8.15 days to control the disease. Similarly, the threshold of vaccination is ρ⁎=0.0084. Therefore, we have to vaccinate at least 80% of susceptible cattle in less than 49.5 days, to control the disease. Using both vaccination and antibiotic treatment, the threshold value of vaccination depends on the rate of antibiotic treatment, αt, and is denoted by ραt. Hence, if 50% of infectious cattle receive antibiotic treatment, then at least 50% of susceptible cattle should get vaccination in less than 73.8 days in order to control the disease.http://dx.doi.org/10.1155/2019/2490313 |
| spellingShingle | Achamyelesh Amare Aligaz Justin Manango W. Munganga Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment Journal of Applied Mathematics |
| title | Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment |
| title_full | Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment |
| title_fullStr | Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment |
| title_full_unstemmed | Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment |
| title_short | Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment |
| title_sort | mathematical modelling of the transmission dynamics of contagious bovine pleuropneumonia with vaccination and antibiotic treatment |
| url | http://dx.doi.org/10.1155/2019/2490313 |
| work_keys_str_mv | AT achamyeleshamarealigaz mathematicalmodellingofthetransmissiondynamicsofcontagiousbovinepleuropneumoniawithvaccinationandantibiotictreatment AT justinmanangowmunganga mathematicalmodellingofthetransmissiondynamicsofcontagiousbovinepleuropneumoniawithvaccinationandantibiotictreatment |