Optimal control of vector-borne diseases: Treatment and prevention

Blayneh, Kbenesh W.; Cao, Yanzhao; Kwon, Hee‐Dae

doi:10.3934/dcdsb.2009.11.587

Cited by 147 publications

(101 citation statements)

References 19 publications

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“…The optimality system is a two-point boundary problem, because of the initial condition of the state system and the terminal condition of the adjoint system [30]. To solve the optimality system with initial conditions for the states and final time conditions for the adjoints, we use the Runge-Kutta fourthorder procedure which is more accurate and elaborative technique.…”

Section: Numerical Simulation Of the Optimal Control Model Results mentioning

confidence: 99%

Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

Kahuru

Luboobi

Nkansah-Gyekye

2017

International Journal of Mathematics and Mathematical Sciences

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Tungiasis is a permanent penetration of female sand flea "Tunga penetrans" into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits.

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Section: Numerical Simulation Of the Optimal Control Model Results mentioning

confidence: 99%

Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

Kahuru

Luboobi

Nkansah-Gyekye

2017

International Journal of Mathematics and Mathematical Sciences

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“…A model for a vertically-transmitted vector-borne disease is formulated extending what is given in [6]. To this end, the host population is grouped into four compartments: susceptible, exposed (no symptom), infectious and treated (or immune) which are denoted by x 1 , x 2 , x 3 and x 4 , respectively and the total population size of the host is N = x 1 + x 2 + x 3 + x 4 .…”

Section: The Main Modelmentioning

confidence: 99%

“…In [6], it is assumed that vectors are exposed after biting only an infectious host, but in this work, a more realistic approach is considered: vectors are assumed to be exposed after they bite (with average contact rate φ per day) an infectious host or a host who is exposed to the disease but asymptomatic and could transmit the disease. This means, infection in the vector population is the sum of two incidence functions namely,…”

Section: The Main Modelmentioning

confidence: 99%

“…This paper is organized as follows. The model studied in [6] is extended to incorporate vertical transmission and density dependent recruitment rate in the host population and an invariant subset of the positive octant is provided in Section (2). In Section (3), an epidemiological threshold is formulated and the asymptotic dynamics of the model, specifically, the existence of a backward bifurcation and the effects of key model parameters, such as, the disease-induced death rate, mosquito-to-human ratio and disease transmission rates is established.…”

Section: Introductionmentioning

confidence: 99%

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Vertically Transmitted Vector-Borne Diseases and the Effects of Extreme Temperature

Blayneh¹

2017

Int. J. of Appl. Math.

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An existing compartmental model of vector-borne diseases is considered to incorporate vertical transmissions in the vector and the host populations. The effects of extrinsic incubation rate of the disease causing pathogen in mosquitoes on the epidemic as well as the endemic nature of the disease are assessed for different values of model parameters. Our numerical simulations indicate that if measures such as personal protection and mosquito control are intensified, then the negative effects of weather-enhanced parameters could be significantly diminished. The effectiveness of these measures is also shown to reduce epidemic levels due to vertical transmissions in the vector as well as the host populations. The existence of a backward bifurcation and its reactions to changes of parameters reacting to temperature increase and the global stability of the disease-free equilibrium, under some conditions are analytically established.

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“…The authors in [13] also used Optimal control to study a nonlinear mathematical SIR epidemic model with a vaccination program. Optimal control was applied to study the impact of chemo-therapy on malaria disease with infective immigrants and the impact of basic amenities [14,15], while [16] studied the effects of prevention and treatment on malaria, using an SEIR model. It was also used in a malaria model with genetically modified mosquitoes but without human population [17].…”

Section: Introductionmentioning

confidence: 99%

Global stability analysis and control of leptospirosis

2016

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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.

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Optimal control of vector-borne diseases: Treatment and prevention

Cited by 147 publications

References 19 publications

Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

Vertically Transmitted Vector-Borne Diseases and the Effects of Extreme Temperature

Global stability analysis and control of leptospirosis

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