Optimal control assessment of Rift Valley fever model with vaccination and environmental sanitation in the presence of treatment delay

Falowo, Olajumoke D.; Olaniyi, Samson; Oladipo, Abiodun Tinuoye

doi:10.1007/s40808-022-01508-1

Cited by 18 publications

(11 citation statements)

References 32 publications

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“…The total cow and mosquito populations are And therefore, we say the region Ω is positively invariant and attracting. This implies that the model in the epidemiogically feasible region Ω is well-posed [10].…”

Section: Model Formulationmentioning

confidence: 99%

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Mathematical Modelling of Lumpy Skin Disease in Dairy Cow

Falowo,

Owolabi,

Oludoun

et al. 2023

IOP Conf. Ser.: Earth Environ. Sci.

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Lumpy skin disease (LSD) is a threatnening disease caused by virus that affects large ruminant animals mainly cattle. LSD is native in many African and Asian countries, having existed for over one hundred years in Africa where it originally started and has recently expanded to the Middle East region. A disease model consisting of six-dimensional system of ordinary differential equations was formulated to properly understand the spread and control of LSD. The classes considered includes the susceptible cow, vaccinated cow, infectious cow, recovered cow, susceptible mosquito and infectious mosquito. This paper captures two modes of transmission of the disease, direct contact and contact through mosquito bites. Inclusion of vaccination parameter makes this model different from existing literature. We show the model is well-posed through positivity and boundedness of the state variables. The basic reproduction number R0 of the model was derived and the disease-free equilibrium points was shown to be locally asymptotically stable when R0 < 1. Sensitivity analysis to identify the most sensitive parameters was conducted and the vaccination parameter was varied using matplotlib module in Python to check the effect of vaccination on both vaccinated and infectious cow. Increase in the vaccination parameter cause the number of vaccinated cow to increase and hence leads to reduction in the number of infected cow.

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Section: Model Formulationmentioning

confidence: 99%

“…Proof. We find the Jacobian matrix of the system (1) evaluated at the disease-free equilibrium E0 Where A = + (r + + ) > 0 , B = (r + + ) > 0 It follows from [10] that the disease-free equilibrium of the model is locally asymptotically stable if 0 < 1 and unstable when 0 > 1.…”

Section: Local Stability Of Disease-free Equilibriummentioning

confidence: 99%

Mathematical Modelling of Lumpy Skin Disease in Dairy Cow

Falowo,

Owolabi,

Oludoun

et al. 2023

IOP Conf. Ser.: Earth Environ. Sci.

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“…At ρ = 2, there correspond quadratic control terms in the pay-off implying continuous controls. To comply with standard in many literature on mathematical models of infectious diseases involving optimal control problems (for example, see Falowo et al (2022) 2022) and some of the references cited therein), ρ is fixed at ρ = 2.…”

Section: Formulation Of Optimal Control Lf Transmission Modelmentioning

confidence: 99%

“…The application of optimal control theory to infectious disease modelling provides insightful information about how the optimal implementation of control interventions can be achieved. Since the application of optimal control theory to disease modelling, there is a significant number of researches in the literature of mathematical modelling of infectious diseases that make use of optimal control theory concept (Falowo et al, 2022;Asamoah et al, 2020Asamoah et al, , 2022Cantor and Ganiats, 1999). However, despite that optimal control theory has provided useful epidemiological insights in ascertaining the optimal control interventions needed to minimize the dynamics of disease transmission in the community at minimum cost of implementation, the number of studies that have made use of mathematical modelling approach to investigate the optimal control of LF transmission dynamics in the literature of mathematical epidemiology is limited (Peter et al, 2020;Higazy et al, 2021;Onah et al, 2020;Ojo et al, 2022;Ibrahim et al, 2021;Musa et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission

Abidemi

Owolabi

Pindza

2022

Physica A: Statistical Mechanics and its Applications

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“…The term effective reproduction number, represented by R ph , is defined as the expected number of secondary cases generated by a single infected individual during the period of infectiousness in a population of susceptible individuals where public health education and hospital treatment are incorporated [36].…”

Section: Tuberculosis Free Equilibrium (Tfe)mentioning

confidence: 99%

Dynamical Behaviour of a Modified Tuberculosis Model with Impact of Public Health Education and Hospital Treatment

Sulayman

Abdullah

2022

Axioms

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Tuberculosis (TB), caused by Mycobacterium tuberculosis is one of the treacherous infectious diseases of global concern. In this paper, we consider a deterministic model of TB infection with the public health education and hospital treatment impact. The effective reproductive number, Rph, that measures the potential spread of TB is presented by employing the next generation matrix approach. We investigate local and global stability of the TB-free equilibrium point, endemic equilibrium point, and sensitivity analysis. The analyses of the proposed model show that the model undergoes the phenomenon of backward bifurcation when the effective reproduction number (Rph) is less than one, where two stable equilibria, namely, the DFE and an EEP coexist. Further, we compute the sensitivity of the impact of each parameter on the effective reproductive number of the model by employing a normalized sensitivity index formula. Numerical simulation of the proposed model was conducted using Maple 2016 and MatLab R2020b software and compared with the theoretical results for illustration purposes. The investigation results can be useful in providing information to policy makers and public health authorities in mitigating the spread of TB infection by public health education and hospital treatment.

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Optimal control assessment of Rift Valley fever model with vaccination and environmental sanitation in the presence of treatment delay

Cited by 18 publications

References 32 publications

Mathematical Modelling of Lumpy Skin Disease in Dairy Cow

Mathematical Modelling of Lumpy Skin Disease in Dairy Cow

Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission

Dynamical Behaviour of a Modified Tuberculosis Model with Impact of Public Health Education and Hospital Treatment

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