Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

Onah, Ifeanyi Sunday; Collins, Obiora Cornelius; Madueme, Praise-God Uchechukwu; Mbah, Godwin C. E.

doi:10.1155/2020/7923125

Cited by 32 publications

(33 citation statements)

References 39 publications

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“…Center manifold theory is widely used to determine the occurrence of forward bifurcation and backward bifurcation at equilibrium point. For instance, bifurcation analysis is performed in the works done in [28][29][30][31][32][33][34][35]. Moreover, based on application of center manifold theory, we have stated an efficient new generalized method to determine a kind of bifurcation that occurs at R 0 � 1 and stability behavior of equilibriums of the model without computing bifurcation parameters required in center manifold theory on bifurcation analysis.…”

Section: Bifurcation and Stability Analysismentioning

confidence: 99%

A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission

Cheneke

Koya

Edessa

2022

International Journal of Mathematics and Mathematical Sciences

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In this study, the co-infection of HIV and cholera model has been developed and analyzed. The new fractional-order derivative is applied and the behavior of the solution is interpreted. The order of new generalized fractional-order derivative implication is presented. A new method is incorporated to determine the forward bifurcation at a threshold R 0 = 1 . The developed method is used to determine the stability of steady-state points. The full model and the submodels’ disease-free equilibrium are locally asymptotically stable if the corresponding reproduction number is less than one and unstable if the production number is greater than one. The only HIV model exhibits forward bifurcation at the threshold point, R 0 = 1 . The numerical simulations solutions obtained using a new generalized fractional-order derivative shows that the total human population size approaches the disease-free equilibrium if the order of the fractional derivative is higher. Also, the simulated results show that the memory effects toward the invading disease are less whenever the order of the fractional derivative is near 0 but higher whenever the order of the fractional derivative is near 1. Furthermore, V. cholerae concentration in the environment increases whenever the intrinsic growth rate increases. The numerical solutions are carried out using MATLAB software.

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Section: Bifurcation and Stability Analysismentioning

confidence: 99%

A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission

Cheneke

Koya

Edessa

2022

International Journal of Mathematics and Mathematical Sciences

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“…Although, Peter et al [11], Onah et al [12] and Ibrahim et al [3] presented an optimal control model of Lassa fever but the virus concentration compartment and periodic rodent population are not considered in their works which is the novelty of this paper. Virus concentration in the environment is considered in this paper due to the faecal droppings and urine discharge by the rodents.…”

Section: Introductionmentioning

confidence: 99%

“…Applying optimal control to infectious disease such as Lassa fever provides important information to public health specialists on how the implementation of control measures minimizes the spread of Lassa fever in the population. Reference literature on infectious diseases that have used the optimal control theory include [13,14,11,12,15,16,17,18]. Based on the suggestions by Bakare et al and the WHO guidelines, this work presents an optimal control theory model for the transmission dynamics of Lassa fever in the presence of control measures such as avoiding hunting of rodents, early treatment and isolation, proper handling of food, rodent control, the wearing of protective clothing when caring for the sick and avoiding contacts with rodents.…”

Section: Introductionmentioning

confidence: 99%

An optimal control model for the transmission dynamics of Lassa fever

Madubueze

Chazuka

2022

Preprint

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In this paper, a mathematical model for Lassa fever transmission dynamics with rodent logistic growth is developed and analysed. The stability analysis of the autonomous system of the model is presented. The sensitivity analysis of the parameters is performed using the Partial Rank Correlation Coefficient (PRCC) technique. The non-autonomous model is further analysed for stability of disease-free periodic equilibrium(DFPE) in terms of reproduction number ratio, $R_{0t}.$ It shown that DFPE is locally asymptotically stable when $R_{0t}<1$ and unstable if $R_{0t}>1$. Additionally, the optimal control model is formulated with five control measures namely; personal protective equipment and avoiding hunting of rodents, proper handling of food, treatment and isolation, cleaning and disinfecting the environment, and rodent control. Simulations of the optimal control model show that the combined implementation of the five control measures reduce Lassa fever spread in the population. However, when there is limited resources to implement the five control measures, three or four combined control measures can be implemented provided that proper handle of food is among the combined control measures.

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“…An age-structured model was proposed by Obabiyi et al [24] for susceptible, exposed, infected and recovered humans. Recovered human population was viewed as permanently immunized in the model of James et al [22] , Onah et al [25] and Obabiyi et al [24] . Recently, Musa et al [26] included quarantined and non-quarantined states both for exposed and infected and introduced a new compartment for hospitalized people.…”

Section: Introductionmentioning

confidence: 99%

A seasonal model to assess intervention strategies for preventing periodic recurrence of Lassa fever

Barua

Dénes

Ibrahim

2021

Heliyon

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Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens prioritized for research and development, affecting several hundreds of thousands of people each year. Lassa fever is spread via infected Natal multimammate mice and also through human-to-human contacts and it is a particular threat to pregnant women. Despite its importance, relatively few mathematical models have been established for modelling Lassa fever transmission up to now. We establish and study a new compartmental model for Lassa fever transmission including asymptomatic carriers, quarantine and periodic coefficients to model annual weather changes. We determine parameter values providing the best fit to data from Nigerian states Edo and Ondo from 2018–20. We perform uncertainty analysis and PRCC analysis to assess the importance of different parameters and numerical simulations to estimate the possible effects of control measures in eradicating the disease. The results suggest that the most important parameter which might be subject of control measures is death rate of mice, while mouse-to-human and human-to-human transmission rates also significantly influence the number of infected. However, decreasing the latter two parameters seems insufficient to eradicate the disease, while a parallel application of decreasing transmission rates and increasing mouse death rate might be able to stop the epidemic.

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Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

Cited by 32 publications

References 39 publications

A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission

A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission

An optimal control model for the transmission dynamics of Lassa fever

A seasonal model to assess intervention strategies for preventing periodic recurrence of Lassa fever

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