Modeling Anthrax with Optimal Control and Cost Effectiveness Analysis

Osman, Shaibu; Otoo, Dominic; Makinde, Oluwole Daniel

doi:10.4236/am.2020.113020

Cited by 16 publications

(3 citation statements)

References 16 publications

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“…In this section, we investigated the sensitivity of the parameters for the basic reproduction of the model using the idea presented in [26][27][28]. It is important to carry out the sensitivity of the basic reproduction number R 0 for its parameters.…”

Section: Sensitivity Analysismentioning

confidence: 99%

A Mathematical Model Analysis for the Transmission Dynamics of Leptospirosis Disease in Human and Rodent Populations

Engida

Theuri

Gathungu

et al. 2022

Computational and Mathematical Methods in Medicine

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This work is aimed at formulating and analyzing a compartmental mathematical model to investigate the impact of rodent-born leptospirosis on the human population by considering a load of pathogenic agents of the disease in an environment and the incidence rate of human infection due to the interaction between infected rodents and the environment. Firstly, the basic properties of the model, the equilibria points, and their stability analysis are studied. We also found the basic reproduction number ( R 0 ) of the model using the next-generation matrix approach. From the stability analysis, we obtained that the disease-free equilibrium (DFE) is globally asymptotically stable if R 0 < 1 and unstable otherwise. The local stability of endemic equilibrium is performed using the phenomenon of the center manifold theory, and the model exhibits forward bifurcation. The most sensitive parameters on the model outcome are also identified using the normalized forward sensitivity index. Finally, numerical simulations of the model are performed to show the stability behavior of endemic equilibrium and the varying effect of the human transmission rates, human recovery rate, and the mortality rate rodents on the model dynamics. The model is simulated using the forward fourth-order Runge-Kutta method, and the results are presented graphically. From graphical stability analysis, we observed that all trajectories of the model solutions evolve towards the unique endemic equilibrium over time when R 0 > 1. Our numerical results revealed that decreasing the transmission rates and increasing the rate of recovery and reduction of the rodent population using appropriate intervention mechanisms have a significant role in reducing the spread of disease infection in the population.

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Section: Sensitivity Analysismentioning

confidence: 99%

A Mathematical Model Analysis for the Transmission Dynamics of Leptospirosis Disease in Human and Rodent Populations

Engida

Theuri

Gathungu

et al. 2022

Computational and Mathematical Methods in Medicine

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“…To rank the implemented strategies in terms of their cost we used cost-effectiveness analysis. To achieve this, we used incremental cost-effectiveness ratio (ICER), which is done dividing the difference of costs between two strategies to the difference of the total number of their infections averted ( Alemneh et al., 2020 ; Osman et al., 2020b ). The total number of infections averted for each strategy is estimated by subtracting total infections with control from without control.…”

Section: Cost-effective Analysismentioning

confidence: 99%

An optimal control model with cost effectiveness analysis of Maize streak virus disease in maize plant

Alemneh

Kassa

Godana

2021

Infectious Disease Modelling

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“…Biological models usually explain the transmission dynamics of infectious diseases and can determine the status of the disease in a population with time. The basic reproduction number is the threshold value that determines the persistence of a disease in a population [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Tuberculosis (TB) with Drug Resistance to First-Line Treatment and Leaky Vaccination: A Deterministic Modelling Perspective

Otoo

Osman

Poku

et al. 2021

Computational and Mathematical Methods in Medicine

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A deterministic model was formulated and employed in the analysis of the dynamics of tuberculosis with a keen emphasis on vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, part of the infected individual after treatment grows resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the next-generation matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity R 0 < 1 , then the disease free equilibrium is stable and unstable if R 0 > 1 . Furthermore, we investigated the optimal prevention, treatment, and vaccination as control measures for the disease. As the objective functional was optimised, there have been a significant reduction in the number of infections and an increase in the number of recovery. The best control measure in combating tuberculosis infections is prevention and vaccination of the susceptible population.

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Modeling Anthrax with Optimal Control and Cost Effectiveness Analysis

Cited by 16 publications

References 16 publications

A Mathematical Model Analysis for the Transmission Dynamics of Leptospirosis Disease in Human and Rodent Populations

A Mathematical Model Analysis for the Transmission Dynamics of Leptospirosis Disease in Human and Rodent Populations

An optimal control model with cost effectiveness analysis of Maize streak virus disease in maize plant

Dynamics of Tuberculosis (TB) with Drug Resistance to First-Line Treatment and Leaky Vaccination: A Deterministic Modelling Perspective

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