Global stability analysis and control of leptospirosis

• Autorzy: Kazeem Oare Okosun , M. Mukamuri , Daniel Oluwole Makinde
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

Słowa kluczowe

EN

Leptospirosis; Stability analysis; Optimal control; Cost-effectiveness analaysis; ANOVA

Kategorie tematyczne

• 92B05: General biology and biomathematics
• 93A30: Mathematical modeling (models of systems, model-matching, etc.)
• 93C15: Systems governed by ordinary differential equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 567-585

Daty

wydano

2016-01-01

otrzymano

2015-10-22

zaakceptowano

2016-06-29

online

2016-08-23

Twórcy

autor

Kazeem Oare Okosun

• Department of Mathematics, Vaal University of Technology,

autor

M. Mukamuri

• Department of Mathematics, Vaal University of Technology,

autor

Daniel Oluwole Makinde

• Faculty of Military Science, University of Stellenbosch,

Identyfikatory

DOI

10.1515/math-2016-0053