Optimal control analysis of Taenia saginata bovine cysticercosis and human taeniasis
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Bovine cysticercosis and human taeniasis are neglected food-borne diseases that pose challenge to
food safety, human health and livelihood of rural livestock farmers. In this paper, we have
formulated and analyzed a deterministic model for transmission dynamics and control of taeniasis
and cysticercosis in humans and cattle respectively. The analysis shows that both the disease free
equilibrium (DFE) and endemic equilibrium (EE) exist. To study the dynamics of the diseases, we
derived the basic reproduction number R0 by next generation matrix method which shows
whether the diseases die or persist in humans and cattle. The diseases clear if R0 < 1 and persist
when R0 > 1. The normalized forward sensitivity index is used to derive sensitive indices of model
parameters. Sensitivity analysis results indicate that human’s and cattle’s recruitment rates,
infection rate of cattle from contaminated environment, probability of humans to acquire
taeniasis due to consumption of infected meat, defecation rate of humans with taeniasis and the
consumption rate of raw or undercooked infected meat are the most positive sensitive parameters
whereas the natural death rates for humans, cattle, Taenia saginata eggs and the proportion of
unconsumed infected meat are the most negative sensitive parameters in diseases’ transmission.
These results suggest that control measures such as improving meat cooking, meat inspection and
treatment of infected humans will be effective for controlling taeniasis and cysticercosis in
humans and cattle respectively. The optimal control theory is applied by considering three time
dependent controls which are improved meat cooking, vaccination of cattle, and treatment of
humans with taeniasis when they are implemented in combination. The Pontryagin’s maximum
principle is adopted to find the necessary conditions for existence of the optimal controls. The
Runge Kutta order four forward-backward sweep method is implemented in Matlab to solve the
optimal control problem. The results indicate that a strategy which focuses on improving meat
cooking and treatment of humans with taeniasis is the optimal strategy for diseases’ control.
Description
Keywords
Human taeniasis Bovine cysticercosis Basic reproduction number Effective reproduction number Optimal control Numerical simulation