Vector Preference Annihilates Backward Bifurcation and Reduces Endemicity

Rivera, Rocio Caja; Barradas, Ignacio

doi:10.1007/s11538-018-00561-1

Cited by 6 publications

(6 citation statements)

References 29 publications

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“…This complication will be empowered if additionally, that new model explicitly incorporates the repellent effect r, making the PTN-induced mortality rate a nonlinear function of r as well. On the other hand, if one considers explicitly the mosquito preference [2,38] to our modeling framework in this manuscript, the resulted model might more harder to study and the result expectations might not be predictable. All these new modeling settings might not lead to monotone disease contact rates and constitute to the new directions of our work that need to be investigated and on which we are already working.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Modeling pyrethroids repellency and its role on the bifurcation analysis for a bed net malaria model

Tsanou

Kamgang

Lubuma

et al. 2020

Chaos, Solitons & Fractals

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Section: Conclusion and Discussionmentioning

confidence: 99%

Modeling pyrethroids repellency and its role on the bifurcation analysis for a bed net malaria model

Tsanou

Kamgang

Lubuma

et al. 2020

Chaos, Solitons & Fractals

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“…The system thresholds are sensitive to variations in parameters of the system. We use the formalism of partial rank correlation coefficient (PRCC) [51][52][53] to characterize the sensitivity of thresholds to variations in systems parameters. To calculate sensitivity to model parameters each parameter is assigned a Gaussian distribution with their respective mean as in table 1 and standard deviation to be 1/30 of the mean (so that neither of the thresholds are eliminated and therefore facilitating their sensitivity analysis).…”

Section: Sensitivity Of System Thresholdsmentioning

confidence: 99%

Complexity and critical thresholds in the dynamics of visceral leishmaniasis

et al. 2020

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We study a general multi-host model of visceral leishmaniasis including both humans and animals, and where host and vector characteristics are captured via host competence along with vector biting preference. Additionally, the model accounts for spatial heterogeneity in human population and heterogeneity in biting behaviour of sandflies. We then use parameters for visceral leishmaniasis in the Indian subcontinent as an example and demonstrate that the model exhibits backward bifurcation, i.e. it has a human infection and a sandfly population threshold, characterized by a bi-stable region. These thresholds shift as a function of host competence, host population size, vector feeding preference, spatial heterogeneity, biting heterogeneity and control efforts. In particular, if control is applied through human treatment a new and lower human infection threshold is created, making elimination difficult to achieve, before eventually the human infection threshold no longer exists, making it impossible to control the disease by only reducing the infection levels below a certain threshold. A better strategy would be to reduce the human infection below a certain threshold potentially by early diagnosis, control animal population levels and keep the vector population under check. Spatial heterogeneity in human populations lowers the overall thresholds as a result of weak migration between patches.

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“…The model in (1) is an extension of models cited in previous studies. 16,29 This mathematical model incorporates the vector feeding preference for infectious hosts ( v > 1) and seasonality on the transmission rate.…”

Section: Mathematical Model (1)mentioning

confidence: 99%

“…In this section, a system of nonautonomous differential equations is used to model the transmission dynamics of cutaneous leishmaniasis in the Peruvian Andes. The model in () is an extension of models cited in previous studies . This mathematical model incorporates the vector feeding preference for infectious hosts ( α v >1) and seasonality on the transmission rate.…”

Section: Modeling Formulationmentioning

confidence: 99%

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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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Vector Preference Annihilates Backward Bifurcation and Reduces Endemicity

Cited by 6 publications

References 29 publications

Modeling pyrethroids repellency and its role on the bifurcation analysis for a bed net malaria model

Modeling pyrethroids repellency and its role on the bifurcation analysis for a bed net malaria model

Complexity and critical thresholds in the dynamics of visceral leishmaniasis

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

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