Mathematical analysis of a lymphatic filariasis model with quarantine and treatment

Mwamtobe, Peter Mpasho; Simelane, Simphiwe; Abelman, Shirley; Tchuenche, Jean M.

doi:10.1186/s12889-017-4160-8

Cited by 19 publications

(18 citation statements)

References 23 publications

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“…Substituting the new value of I * h in (11.5), we have 11) From the sixth equation in (4.1), setting the right hand side to zero, we have (11.12) From the seventh equation in (4.1), setting the right hand side to zero and substituting the value of S * v , we have…”

Section: Acknowledgementmentioning

confidence: 99%

“…[10] developed and analysed a mathematical model to quantify the potential effect that heterogeneous infection processes occurring in the major mosquito vector genera may have on parasite transmission and control. [11] formulated and analysed a deterministic differential equation model with two key control measures; quarantine and treatment. They assumed that no infection exists at the initial stage and that there is no vertical transmission in both human and mosquito population.…”

Section: Introductionmentioning

confidence: 99%

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Global Stability and Backward Bifurcation for a Lymphatic filariasis model

Iyare

Okuonghae

Osagiede

2021

Preprint

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An ODE model of Lymphatic filariasis is proposed with eight mutually disjoint compartments. The model is proven to be mathematically and epidemiologically well posed. Epidemiological interpretation of the effective reproduction number is presented. A special case is considered where the death rate due to the disease is negligible. An endemic equilibrium under this special scenario is explicitly computed and the presence of backward bifurcation under this condition is suggested. Bifurcation analysis is performed using the Castillo-Chavez and Song theorem in the special case where death due to disease is zero. When the re-infection rate is zero, backward bifurcation is shown not to be present. In such a situation, global asymptotic stability of the endemic equilibrium is established.

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Section: Acknowledgementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global Stability and Backward Bifurcation for a Lymphatic filariasis model

Iyare

Okuonghae

Osagiede

2021

Preprint

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“…α+δ+µ b represents the average number of secondary bird (mosquito) infections that one infectious mosquito (bird) generates in a totally susceptible bird (mosquito) population during the entire duration of its infectiousness. The basic reproduction number also provides important information for preventing and controlling the spread of the infection (Mwamtobe et al 2017).…”

Section: The Basic Reproduction Numbermentioning

confidence: 99%

Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds

Maliyoni

2020

Acta Biotheor

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Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finitetime to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes.

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“…In a 2016 study, Iddi et al assessed the impact of MDA, health education campaigns and the vector control sterile insect technique on the transmission dynamics of LF using a deterministic model [51]. In 2017, Mwamtobe et al proposed an SEI-SI LF model with quarantine and treatment as control strategies [52]. In these studies, the parameter values are either assumed or obtained from existing malaria models.…”

Section: Introductionmentioning

confidence: 99%

A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, the Philippines

Salonga

Mendoza

et al. 2021

R. Soc. open sci.

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Despite being one of the first countries to implement mass drug administration (MDA) for elimination of lymphatic filariasis (LF) in 2001 after a pilot study in 2000, the Philippines is yet to eliminate the disease as a public health problem with 6 out of the 46 endemic provinces still implementing MDA for LF as of 2018. In this work, we propose a mathematical model of the transmission dynamics of LF in the Philippines and a control strategy for its elimination using MDA. Sensitivity analysis using the Latin hypercube sampling and partial rank correlation coefficient methods suggests that the infected human population is most sensitive to the treatment parameters. Using the available LF data in Caraga Region from the Philippine Department of Health, we estimate the treatment rates r 1 and r 2 using the least-squares parameter estimation technique. Parameter bootstrapping showed small variability in the parameter estimates. Finally, we apply optimal control theory with the objective of minimizing the infected human population and the corresponding implementation cost of MDA, using the treatment coverage γ as the control parameter. Simulation results highlight the importance of maintaining a high MDA coverage per year to effectively minimize the infected population by the year 2030.

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Mathematical analysis of a lymphatic filariasis model with quarantine and treatment

Cited by 19 publications

References 23 publications

Global Stability and Backward Bifurcation for a Lymphatic filariasis model

Global Stability and Backward Bifurcation for a Lymphatic filariasis model

Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds

A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, the Philippines

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