Global stability and optimal control of melioidosis transmission model with hygiene care and treatment in human and animal populations

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

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Global stability and optimal control for a tuberculosis model with vaccination and treatment

Discrete and Continuous Dynamical Systems - Series B ◽

10.3934/dcdsb.2016.21.1009 ◽

2016 ◽

Vol 21 (3) ◽

pp. 1009-1022 ◽

Cited By ~ 13

Author(s):

Yali Yang ◽

Sanyi Tang ◽

Xiaohong Ren ◽

Huiwen Zhao ◽

Chenping Guo

Keyword(s):

Optimal Control ◽

Global Stability ◽

Tuberculosis Model

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Evaluation of the immunogenicity and efficacy of BCG and MTBVAC vaccines using a natural transmission model of tuberculosis

Veterinary Research ◽

10.1186/s13567-019-0702-7 ◽

2019 ◽

Vol 50 (1) ◽

Cited By ~ 3

Author(s):

Alvaro Roy ◽

Irene Tomé ◽

Beatriz Romero ◽

Víctor Lorente-Leal ◽

José A. Infantes-Lorenzo ◽

...

Keyword(s):

Animal Models ◽

Lymph Nodes ◽

Interferon Gamma ◽

Model System ◽

Transmission Model ◽

Control Group ◽

Animal Populations

Abstract Effective vaccines against tuberculosis (TB) are needed in order to prevent TB transmission in human and animal populations. Evaluation of TB vaccines may be facilitated by using reliable animal models that mimic host pathophysiology and natural transmission of the disease as closely as possible. In this study, we evaluated the immunogenicity and efficacy of two attenuated vaccines, BCG and MTBVAC, after each was given to 17 goats (2 months old) and then exposed for 9 months to goats infected with M. caprae. In general, MTBVAC-vaccinated goats showed higher interferon-gamma release than BCG vaccinated goats in response to bovine protein purified derivative and ESAT-6/CFP-10 antigens and the response was significantly higher than that observed in the control group until challenge. All animals showed lesions consistent with TB at the end of the study. Goats that received either vaccine showed significantly lower scores for pulmonary lymph nodes and total lesions than unvaccinated controls. Both MTBVAC and BCG vaccines proved to be immunogenic and effective in reducing severity of TB pathology caused by M. caprae. Our model system of natural TB transmission may be useful for evaluating and optimizing vaccines.

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An optimal control problem arising from a dengue disease transmission model

Mathematical Biosciences ◽

10.1016/j.mbs.2012.11.014 ◽

2013 ◽

Vol 242 (1) ◽

pp. 9-16 ◽

Cited By ~ 48

Author(s):

Dipo Aldila ◽

Thomas Götz ◽

Edy Soewono

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Disease Transmission ◽

Transmission Model ◽

Dengue Disease ◽

Disease Transmission Model

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Stability, Bifurcation and Optimal Control Analysis of a Malaria Model in a Periodic Environment

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0221 ◽

2018 ◽

Vol 19 (6) ◽

pp. 627-642 ◽

Cited By ~ 2

Author(s):

Prabir Panja ◽

Shyamal Kumar Mondal ◽

Joydev Chattopadhyay

Keyword(s):

Optimal Control ◽

Disease Transmission ◽

Existence Condition ◽

Infected Mosquito ◽

Transmission Model ◽

Control Analysis ◽

Periodic Environment ◽

Vector Population ◽

Autonomous Case ◽

Disease Transmission Model

AbstractIn this paper, a malaria disease transmission model has been developed. Here, the disease transmission rates from mosquito to human as well as human to mosquito and death rate of infected mosquito have been constituted by two variabilities: one is periodicity with respect to time and another is based on some control parameters. Also, total vector population is divided into two subpopulations such as susceptible mosquito and infected mosquito as well as the total human population is divided into three subpopulations such as susceptible human, infected human and recovered human. The biologically feasible equilibria and their stability properties have been discussed. Again, the existence condition of the disease has been illustrated theoretically and numerically. Hopf-bifurcation analysis has been done numerically for autonomous case of our proposed model with respect to some important parameters. At last, a optimal control problem is formulated and solved using Pontryagin’s principle. In numerical simulations, different possible combination of controls have been illustrated including the comparisons of their effectiveness.

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