Zoonotic visceral leishmaniasis transmission: modeling, backward bifurcation, and optimal control

Zhao, Song-Feng; Kuang, Yan; Wu, Chih-Hang John; Ben‐Arieh, David; Ramalho-Ortigão, Marcelo; Bi, Kaiming

doi:10.1007/s00285-016-0999-z

Cited by 42 publications

(40 citation statements)

References 21 publications

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“…In this most recent paper, we were able to fit the model to real data from Araçatuba/SP city (Brazil), carrying out a very robust model and results. And, besides those models published by our research team, we also have other researchers who published mathematical models for LVZ, as Zhao et al [13], in which their model differs from ours by the adopted mathematical structure and the presence of backward bifurcation.…”

Section: Introductionmentioning

confidence: 91%

The Preventive Control of Zoonotic Visceral Leishmaniasis: Efficacy and Economic Evaluation

Shimozako

Massad

2017

Computational and Mathematical Methods in Medicine

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Zoonotic Visceral Leishmaniasis (ZVL) is one of the world's deadliest and neglected infectious diseases, according to World Health Organization. This disease is one of major human and veterinary medical significance. The sandfly and the reservoir in urban areas remain among the major challenges for the control activities. In this paper, we evaluated five control strategies (positive dog elimination, insecticide impregnated dog collar, dog vaccination, dog treatment, and sandfly population control), considering disease control results and cost-effectiveness. We elaborated a mathematical model based on a set of differential equations in which three populations were represented (human, dog, and sandfly). Humans and dogs were divided into susceptible, latent, clinically ill, and recovery categories. Sandflies were divided into noninfected, infected, and infective. As the main conclusions, the insecticide impregnated dog collar was the strategy that presented the best combination between disease control and cost-effectiveness. But, depending on the population target, the control results and cost-effectiveness of each strategy may differ. More and detailed studies are needed, specially one which optimizes the control considering more than one strategy in activity.

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Section: Introductionmentioning

confidence: 91%

The Preventive Control of Zoonotic Visceral Leishmaniasis: Efficacy and Economic Evaluation

Shimozako

Massad

2017

Computational and Mathematical Methods in Medicine

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“…This means

R_{0} < 1

would not be sufficient for the eradication of the disease. We use realistic epidemiological parameters from Peru (Table ) for numerical simulations (bifurcation diagrams); Garba et al and Zhao et al do not use realistic epidemiological parameter values from any specific country or region. This is the first time that bifurcation phenomena have been theoretically and numerically reported in the transmission dynamics of cutaneous leishmaniasis in Peru.…”

Section: Discussionmentioning

confidence: 99%

“…Remark The approach in this work to prove existence of endemic equilibria and backward bifurcation differs from the work presented by Garba et al and Zhao et al in the following: ‐They concentrate in numerical results with generic values, not specific ones. Moreover, their analysis does not make any use of threshold parameters.…”

Section: Modeling and Analysis For Cutaneous Leishmaniasis In Perumentioning

confidence: 99%

“…We are focused on the dynamic of cutaneous leishmaniasis, but it should be noted that this model (1) describes the dynamic of other vector-borne diseases. There is a wide literature about this type of vector-host models in the literature [7][8][9][10][11][12][13]15,16 that can be used for modeling vector-borne diseases that are caused by microparasites. The model presented here is a particular case of the visceral leishmaniasis model presented by Zhao et al 16 and the dengue model presented by Garba et al, 15 and it is an extension of the cutaneous leishmaniasis SI-SI model of Biswas et al 9 At the end of this section we will explain in which extent our model and analysis differs from the work of Zhao et al 16 and Garba et al 15 Cutaneous leishmaniasis is a skin infection that is caused by "Leishmania" microparasite protozoa that is transmitted by the bite of female sandflies.…”

Section: Modeling and Analysis For Cutaneous Leishmaniasis In Perumentioning

confidence: 99%

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Cutaneous leishmaniasis in Peru using a vector‐host model: Backward bifurcation and sensitivity analysis

Barradas

Rivera

2018

Math Methods in App Sciences

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The final goal of control policies in neglected vector‐borne diseases in developing countries is to protect humans. These vector‐borne diseases include leishmaniasis, dengue, chagas, and malaria. The traditional control measures for vector‐borne diseases, as with any other illnesses, suggest to reduce the basic reproduction number R0 below the value 1. This strategy is not necessarily sufficient when a backward bifurcation occurs. Because of its worldwide relevance, we are interested in modeling cutaneous leishmaniasis with Peru as a specific example. We use a vector‐host model with an extrinsic incubation period, which gives evidence that a backward bifurcation can occur under certain conditions. We estimate some parameters for the cutaneous leishmaniasis model in Peru. The uncertainty of the parameters suggests that we cannot guarantee the avoidance of a backward bifurcation range. It is important to be attentive to the appearance of phenomena that could make eradication more difficult. Local and global sensitivity analyses agree that R0 is most sensitive to the number of bites by a female sandfly and its natural mortality rate. The former dependency suggests very practical control policies.

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“…For a future research, we plan to develop an agent-based model [24] [25] [26] to simulate interactions and predict the key parameters in order to offer suggestions on controlling the number of predators. Also, future expansion of this research can consider applying optimal control theory [27] [28] to provide decision makers with better policies of controlling the population of the two-spotted spider mites. Spatial games which have been adopted to analyze various structure of populations [29] [30], also present a future expansion of our research.…”

Section: Discussionmentioning

confidence: 99%

Mathematical Model for Two-Spotted Spider Mites System: Verification and Validation

Kuang¹,

Ben‐Arieh²,

Zhao³

et al. 2017

OJMSi

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This paper presents and compares four mathematical models with unique spatial effects for a prey-predator system, with Tetranychus urticae as prey and Phytoseiulus persimilis as predator. Tetranychus urticae, also known as two-spotted spider mite, is a harmful plant-feeding pest that causes damage to over 300 species of plants. Its predator, Phytoseiulus persimilis, a mite in the Family Phytoseiidae, effectively controls spider mite populations. In this study, we compared four mathematical models using a numerical simulation. These models include two known models: self-diffusion, and cross-diffusion, and two new models: chemotaxis effect model, and integro diffusion model, all with a Beddington-De Angelis functional response. The modeling results were validated by fitting experimental data. Results demonstrate that interaction scheme plays an important role in the prey-predator system and that the crossdiffusion model fits the real system best. The main contribution of this paper is in the two new models developed, as well as the validation of all the models using experimental data.

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Zoonotic visceral leishmaniasis transmission: modeling, backward bifurcation, and optimal control

Cited by 42 publications

References 21 publications

The Preventive Control of Zoonotic Visceral Leishmaniasis: Efficacy and Economic Evaluation

The Preventive Control of Zoonotic Visceral Leishmaniasis: Efficacy and Economic Evaluation

Cutaneous leishmaniasis in Peru using a vector‐host model: Backward bifurcation and sensitivity analysis

Mathematical Model for Two-Spotted Spider Mites System: Verification and Validation

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