Analysis of Listeriosis Transmission Dynamics with Optimal Control

Taeniasis and cysticercosis pose a significant challenge to food safety and public health. Cysticercosis reduces the market value for pigs and cattle by making pork and beef unsafe for consumption. In this paper, a mathematical model for the transmission dynamics of taeniasis and cysticercosis in humans, pigs and cattle is formulated and analyzed. The analysis shows that both the disease free equilibrium (DFE) and the endemic equilibrium (EE) exist. To study the dynamics of the diseases, we derived the basic reproduction number $R_{0}$ R 0 by next generation matrix method. When $R_{0}< 1$ R 0 < 1 , the DFE is globally asymptotically stable whereas when $R_{0} > 1$ R 0 > 1 the EE is globally asymptotically stable. The normalized forward sensitivity index was used to determine sensitive parameters to the diseases. Humans’ recruitment rate, probability of humans’ infection with taeniasis and the defecation rate of taenia eggs by humans with taeniasis are the most positive sensitive parameters to diseases’ transmission whereas the human natural death rate is the most negative sensitive parameter. However, it is biologically unethical and not practical to increase human natural mortality rate for disease control. In this case, other parameters with negative sensitivity indices such as death rate of taenia eggs and proportions of unconsumed infected beef and pork can be considered for disease control. Generally, to control the diseases, more efforts should be made directed to reducing the number of humans who have taeniasis and defecate in the open environment. Also meat inspection and indoor keeping of cattle and pigs should be emphasized.

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“…Proof Since the endemic equilibrium exists if and only if R 0 > 1, we adopt the approach in Osman et al [26]…”

Section: Global Stability Of the Endemic Equilibrium (E * )mentioning

confidence: 99%

Modeling and analysis of taeniasis and cysticercosis transmission dynamics in humans, pigs and cattle

Mwasunda

Irunde²,

Kajunguri

et al. 2021

Adv Differ Equ

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“…In order to achieve this, the following objective functional is considered:

where t f is the final time, d 1 and d 2 are balancing constant coefficients of the infected maize and infected leafhopper respectively while w 1 , w 2 and w 3 are weight coefficients for each individual control measure. We choose a nonlinear cost on the controls based on the assumption that the cost takes nonlinear form ( Alemneh, 2020 ; Alemneh et al., 2020 ; Osman et al., 2020a ). The goal is to find the optimal control triple (

) such that:

where the control set

is measurable on [0, t f ],

.…”

Section: Existence Of Optimal Controlmentioning

confidence: 99%

An optimal control model with cost effectiveness analysis of Maize streak virus disease in maize plant

Alemneh

Kassa

Godana

2021

Infectious Disease Modelling

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“…The objective is to adjust these optimal controls so as to optimize the given objective function. Over the past two decades, a number of mathematical models have been formulated and analyzed to determine the optimal control strategies for various infectious diseases ( Asamoah et al, 2020 , Khan et al, 2020 , Nyerere et al, 2020 , Okosun et al, 2016 , Osman et al, 2020 , Tilahun et al, 2017 ). In particular, there are only a few deterministic models that have been formulated and analyzed to study the transmission dynamics and control of taeniasis and cysticercosis in humans and pigs due to Taenia solium tapeworm parasite.…”

Section: Introductionmentioning

confidence: 99%

Optimal control analysis of Taenia saginata bovine cysticercosis and human taeniasis

Mwasunda

Irunde²,

Kajunguri

et al. 2022

Parasite Epidemiology and Control

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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 R 0 by next generation matrix method which shows whether the diseases die or persist in humans and cattle. The diseases clear if R 0 < 1 and persist when R 0 > 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.

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Analysis of Listeriosis Transmission Dynamics with Optimal Control

Cited by 19 publications

References 24 publications

Modeling and analysis of taeniasis and cysticercosis transmission dynamics in humans, pigs and cattle

Modeling and analysis of taeniasis and cysticercosis transmission dynamics in humans, pigs and cattle

An optimal control model with cost effectiveness analysis of Maize streak virus disease in maize plant

Optimal control analysis of Taenia saginata bovine cysticercosis and human taeniasis

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