A Mathematical Model to Control the Prevalence of a Directly and Indirectly Transmitted Disease

Begoña Cantó, Carmen Coll, Maria Jesús Pagán, Joan Poveda and Elena Sánchez
Additional contact information
Begoña Cantó: Institut de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46071 València, Spain
Carmen Coll: Institut de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46071 València, Spain
Maria Jesús Pagán: Grupo de Investigación e Innovación Alimentaria, Universitat Politècnica de València, 46071 València, Spain
Joan Poveda: Grupo de Investigación e Innovación Alimentaria, Universitat Politècnica de València, 46071 València, Spain
Elena Sánchez: Institut de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46071 València, Spain

Mathematics, 2021, vol. 9, issue 20, 1-15

Abstract: In this paper, a mathematical model to describe the spread of an infectious disease on a farm is developed. To analyze the evolution of the infection, the direct transmission from infected individuals and the indirect transmission from the bacteria accumulated in the enclosure are considered. A threshold value of population is obtained to assure the extinction of the disease. When this size of population is exceeded, two control procedures to apply at each time are proposed. For each of them, a maximum number of steps without control and reducing the prevalence of disease is obtained. In addition, a criterion to choose between both procedures is established. Finally, the results are numerically simulated for a hypothetical outbreak on a farm.

Keywords: epidemic model; direct and indirect transmission; discrete-time system; stability; control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/20/2562/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/20/2562/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:20:p:2562-:d:655054

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().