# Global stability analysis and control of leptospirosis

Kazeem Oare Okosun; M. Mukamuri; Daniel Oluwole Makinde

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 567-585
- ISSN: 2391-5455

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topKazeem Oare Okosun, M. Mukamuri, and Daniel Oluwole Makinde. "Global stability analysis and control of leptospirosis." Open Mathematics 14.1 (2016): 567-585. <http://eudml.org/doc/286759>.

@article{KazeemOareOkosun2016,

abstract = {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.},

author = {Kazeem Oare Okosun, M. Mukamuri, Daniel Oluwole Makinde},

journal = {Open Mathematics},

keywords = {Leptospirosis; Stability analysis; Optimal control; Cost-effectiveness analaysis; ANOVA; leptospirosis; stability analysis; optimal control; cost-effectiveness analaysis},

language = {eng},

number = {1},

pages = {567-585},

title = {Global stability analysis and control of leptospirosis},

url = {http://eudml.org/doc/286759},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Kazeem Oare Okosun

AU - M. Mukamuri

AU - Daniel Oluwole Makinde

TI - Global stability analysis and control of leptospirosis

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 567

EP - 585

AB - 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.

LA - eng

KW - Leptospirosis; Stability analysis; Optimal control; Cost-effectiveness analaysis; ANOVA; leptospirosis; stability analysis; optimal control; cost-effectiveness analaysis

UR - http://eudml.org/doc/286759

ER -

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