Journal of Applied Mathematics

Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment

Achamyelesh Amare Aligaz and Justin Manango W. Munganga

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Abstract

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.

Article information

Source
J. Appl. Math., Volume 2019 (2019), Article ID 2490313, 10 pages.

Dates
Received: 18 September 2018
Revised: 16 December 2018
Accepted: 3 January 2019
First available in Project Euclid: 15 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.jam/1552615280

Digital Object Identifier
doi:10.1155/2019/2490313

Citation

Aligaz, Achamyelesh Amare; Munganga, Justin Manango W. Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatment. J. Appl. Math. 2019 (2019), Article ID 2490313, 10 pages. doi:10.1155/2019/2490313. https://projecteuclid.org/euclid.jam/1552615280


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