A Mathematical Approach to Control Cutaneous Leishmaniasis Through Insecticide Spraying

Biswas, Dibendu; Kesh, Dipak; Datta, Abhirup; Chatterjee, Amar Nath; Roy, Priti Kumar

doi:10.15764/am.2014.02005

Cited by 9 publications

(10 citation statements)

References 12 publications

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“…The model framework allows 2 modes of transmission, one for human hosts and the other one for female sandflies ( Lutzomyias ). This model is an extension of the SI‐SI cutaneous leishmaniasis model of Biswas et al…”

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%

“…A greatly increased knowledge of the Leishmania species involved and of their natural hosts is helping to define the nature and extent of the disease . Some recent mathematical modeling of cutaneous leishmaniasis from the eastern hemisphere can be found in the literature . The main novelty of this manuscript is the mathematical modeling of cutaneous leishmaniasis in Peru, a country in the western hemisphere and the mathematical methods used for the analysis.…”

Section: Introductionmentioning

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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Section: Modeling and Analysis For Cutaneous Leishmaniasis In Perumentioning

confidence: 99%

Section: Modeling and Analysis For Cutaneous Leishmaniasis In Perumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…They discussed the role of more than one reservoir population and how it could affect the disease transmission depending on host preferences and biting intensity. Biswas et al [15] developed different models of cutaneous leishmaniasis consisting of different aspects of the disease transmission. We have previously considered susceptible and infected human and vector populations with the target of reducing the vector population so that the disease can be controlled.…”

Section: Introductionmentioning

confidence: 99%

“…Above, the optimal controls u * 1 , u * 2 , u * 3 , u * 4 are functions of time t, and all the phase variables in formulae (11), (15), (19), and (23) correspond to these optimal solutions of the state system (4).…”

mentioning

confidence: 99%

Cost-Effective Analysis of Control Strategies to Reduce the Prevalence of Cutaneous Leishmaniasis, Based on a Mathematical Model

Biswas

Dolai

Chowdhury

et al. 2018

MCA

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Leishmaniasis is a neglected tropical vector-borne epidemic disease, and its transmission is a complex process. Zoonotic transmission to humans or animals occurs through the bites of female Phlebotominae sand flies. Here, reservoir is considered as a major source of endemic pathogen pool for disease outbreak, and the role of more than one reservoir animal becomes indispensable. To study the role of the reservoir animals on disease dynamics, a mathematical model was constructed consisting of susceptible and infected populations of humans and two types of reservoir (animal) and vector populations, respectively. Our aim is to prevent the disease by applying a control theoretic approach, when more than one type of reservoir animal exists in the region. We use drugs like sodium stibogluconate and meglumine antimoniate to control the disease for humans and spray insecticide to control the sand fly population. Similarly, drugs are applied for infected reservoir animals of Types A and B. We calculated the cost-effectiveness of all possible combinations of the intervention and control policies. One of our findings is that the most cost-effective case for Leishmania control is the spray of insecticides for infected sand fly vector. Alternate strategic cases were compared to address the critical shortcomings of single strategic cases, and a range of control strategies were estimated for effective control and economical benefit of the overall control strategy. Our findings provide the most innovative techniques available for application to the successful eradication of cutaneous leishmaniasis in the future.

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How vector feeding preference through an infectious host relates to the seasonal transmission rates in a mathematical vector‐host model

Rivera

2019

Math Methods in App Sciences

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Vector-borne diseases, such as leishmaniasis, dengue, malaria, and yellow fever, transmitted by microparasites show periodic fluctuations in their prevalence.The novelty of this research is to assess the relationship between the vector feeding preference for an infectious host and the annual seasonal transmission through a vector-host mathematical model. For the first time, numerical simulations illustrate that by increasing the vector feeding preference value in the transmission dynamics, periodic fluctuations accentuate and the endemic equilibrium average increases in vector and host populations. Moreover, increasing the vector feeding preference value, the amplitude strengthens for the infectious host and vector populations. This periodic behavior shows a similar pattern with the Peruvian incidence data from 2000 to 2016 for Andean cutaneous leishmaniasis provided by the Ministry of Health of Peru (MINSA). In addition, using the Floquet theory, the time average method and the linear operator method provides for the first time that the basic reproduction number  0 for a nonautonomous system depends explicitly on the vector feeding preference for the infectious host. The nonautonomous model system shows that  0 is a threshold parameter for the local stability of the disease-free periodic solution. Therefore, the vector feeding preference is an important factor that should be considered and attended to for future research. Public and veterinary health in Peru and other countries should consider the vector feeding preference for specific host to vector control. KEYWORDS cutaneous leishmaniasis, host, seasonal transmission rate, vector-borne diseases, vector feeding preference MSC CLASSIFICATION 92B05

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A Mathematical Approach to Control Cutaneous Leishmaniasis Through Insecticide Spraying

Cited by 9 publications

References 12 publications

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

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

Cost-Effective Analysis of Control Strategies to Reduce the Prevalence of Cutaneous Leishmaniasis, Based on a Mathematical Model

How vector feeding preference through an infectious host relates to the seasonal transmission rates in a mathematical vector‐host model

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