Dynamic Study of SIQR-B Fractional-Order Epidemic Model of Cholera with Optimal Control Strategies in Mayo-Tsanaga Department of Cameroon Far North Region

Nguiwa, Tchule; Justin, Mibaile; Djaouda, Moussa; Betchewe, Gambo; Mohamadou, Alidou

doi:10.1142/s1793048020500071

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…In fact, Cole [ 17 ] deduced that biological cell membranes possess fractional-order conductivity, so the model of the biological systems are supposed to partition in groups of non-integer order. Currently, there is considerable research on the applications of the fractional-order derivatives in describing different various diseases, such as malaria [ 18 ], dengue fever [ 16 ], Ebola [ 19 ], Covid-19 [ 20 ], HIV-AIDS [ 21 ], measles [ 22 ], cholera [ 23 , 24 ], and so on.…”

Section: Introductionmentioning

confidence: 99%

A fractional SVIR-B epidemic model for Cholera with imperfect vaccination and saturated treatment

2022

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Given the limited medical resources in most cholera endemic countries, in this paper, a nonlinear fractional SVIR-B (Susceptible-Vaccinated-Infected-Recovered, Bacterial) cholera epidemic model with imperfect vaccination and saturated treatment is proposed and investigated. The model performs well-posed in both epidemiologically and mathematically, especially, we demonstrate the positivity and boundedness of all solutions using the generalized mean value theorem. The control reproduction number is derived using the next generation matrix method and both local and global stability analyses for the disease-free equilibrium is performed by analyzing the characteristic equation and using Lyapunov functional. Then, the existence and stability of endemic equilibria are further addressed. Sufficient conditions for the existence of backward bifurcation and Hopf bifurcation are also derived. Subsequently, an optimal control problem with vaccination, media coverage, treatment, and sanitation as control strategies is proposed and analyzed, providing a rationale for cholera control and prevention. In addition, several numerical examples are employed to illustrate our theoretical results.

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Section: Introductionmentioning

confidence: 99%

A fractional SVIR-B epidemic model for Cholera with imperfect vaccination and saturated treatment

2022

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Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

et al. 2021

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In this study, a novel reaction–diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19 SEIR model with nonlinear incidence rates by taking into account the effects of random movements of individuals from different compartments in their environments. The equilibrium points of the new system are found for both diffusive and non-diffusive models, where a detailed stability analysis is conducted for them. Moreover, the stability regions in the space of parameters are attained for each equilibrium point for both cases of the model and the effects of parameters are explored. A numerical verification for the proposed model using a finite difference-based method is illustrated along with their consistency, stability and proving the positivity of the acquired solutions. The obtained results reveal that the random motion of individuals has significant impact on the observed dynamics and steady-state stability of the spread of the virus which helps in presenting some strategies for the better control of it.

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Cholera disease dynamics with vaccination control using delay differential equation

Singh,

Kumar,

Akgül

et al. 2024

Sci Rep

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The COVID-19 pandemic came with many setbacks, be it to a country’s economy or the global missions of organizations like WHO, UNICEF or GTFCC. One of the setbacks is the rise in cholera cases in developing countries due to the lack of cholera vaccination. This model suggested a solution by introducing another public intervention, such as adding Chlorine to water bodies and vaccination. A novel delay differential model of fractional order was recommended, with two different delays, one representing the latent period of the disease and the other being the delay in adding a disinfectant to the aquatic environment. This model also takes into account the population that will receive a vaccination. This study utilized sensitivity analysis of reproduction number to analytically prove the effectiveness of control measures in preventing the spread of the disease. This analysis provided the mathematical evidence for adding disinfectants in water bodies and inoculating susceptible individuals. The stability of the equilibrium points has been discussed. The existence of stability switching curves is determined. Numerical simulation showed the effect of delay, resulting in fluctuations in some compartments. It also depicted the impact of the order of derivative on the oscillations.

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Dynamic Study of SIQR-B Fractional-Order Epidemic Model of Cholera with Optimal Control Strategies in Mayo-Tsanaga Department of Cameroon Far North Region

Cited by 3 publications

References 14 publications

A fractional SVIR-B epidemic model for Cholera with imperfect vaccination and saturated treatment

A fractional SVIR-B epidemic model for Cholera with imperfect vaccination and saturated treatment

Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

Cholera disease dynamics with vaccination control using delay differential equation

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