Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV

Omame, Andrew; Abbas, Mujahid; Onyenegecha, Chibueze P.

doi:10.1016/j.rinp.2022.105481

Cited by 53 publications

(16 citation statements)

References 36 publications

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“…The initial conditions in ( 18) is used to solve the state system forward in time using the MATLAB built-in ODE45 routine. Next, the adjoint system is solved using the transversality condition (22) and the approximated solution of the state system. Then, the values of the control variables are computed using the control characterization in (23), and the control set u * is updated via a convex combination of previous and current values of the control characterization.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…To understand the dynamics of co‐interaction between diseases, a lot of models have been proposed in the literature. 22 , 23 , 24 , 25 , 26 , 27 , 28 The authors in Reference 22 considered a dynamical model for SARS‐CoV‐2 and zika virus, incorporating the assumption of incident co‐infection with the two diseases. They showed that under this scenario, the qualitative behavior of the complete co‐infection model is not driven by that of the sub‐models.…”

Section: Introductionmentioning

confidence: 99%

“…To understand the dynamics of co‐interaction between diseases, a lot of models have been proposed in the literature 22‐28 22 considered a dynamical model for SARS‐CoV‐2 and zika virus, incorporating the assumption of incident co‐infection with the two diseases.…”

Section: Introductionmentioning

confidence: 99%

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An optimal control model for COVID‐19, zika, dengue, and chikungunya co‐dynamics with reinfection

Omame

Isah

Abbas

2022

Optim Control Appl Methods

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The co‐circulation of different emerging viral diseases is a big challenge from an epidemiological point of view. The similarity of symptoms, cases of virus co‐infection, and cross‐reaction can mislead in the diagnosis of the disease. In this article, a new mathematical model for COVID‐19, zika, chikungunya, and dengue co‐dynamics is developed and studied to assess the impact of COVID‐19 on zika, dengue, and chikungunya dynamics and vice‐versa. The local and global stability analyses are carried out. The model is shown to undergo a backward bifurcation under a certain condition. Global sensitivity analysis is also performed on the parameters of the model to determine the most dominant parameters. If the zika‐related reproduction number is used as the response function, then important parameters are: the effective contact rate for vector‐to‐human transmission of zika ( , which is positively correlated), the human natural death rate ( , positively correlated), and the vector recruitment rate ( , also positively correlated). In addition, using the class of individuals co‐infected with COVID‐19 and zika ( ) as response function, the most dominant parameters are: the effective contact rate for COVID‐19 transmission ( , positively correlated), the effective contact rate for vector‐to‐human transmission of zika ( , positively correlated). To control the co‐circulation of all the diseases adequately under an endemic setting, time dependent controls in the form of COVID‐19, zika, dengue, and chikungunya preventions are incorporated into the model and analyzed using the Pontryagin's principle. The model is fitted to real COVID‐19, zika, dengue, and chikungunya datasets for Espirito Santo (a city with the co‐circulation of all the diseases), in Brazil and projections made for the cumulative cases of each of the diseases. Through simulations, it is shown that COVID‐19 prevention could greatly reduce the burden of co‐infections with zika, dengue, and chikungunya. The negative impact of the COVID‐19 pandemic on the control of the arbovirus diseases is also highlighted. Furthermore, it is observed that prevention controls for zika, dengue, and chikungunya can significantly reduce the burden of co‐infections with COVID‐19.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An optimal control model for COVID‐19, zika, dengue, and chikungunya co‐dynamics with reinfection

Omame

Isah

Abbas

2022

Optim Control Appl Methods

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“…Namun tidak berakhir pada tahun tersebut, akhir tahun 2019 kemunculan COVID-19 yang sama-sama disebabkan oleh virus corona, membuat banyak penelitian model matematika MERS-CoV dijadikan sebagai acuan. Terbaru akan terbit Juni 2022, bifurkasi transkritikal pada model penyakit COVID-19 dianalisa oleh [6] dan [7].…”

Section: Pendahuluanunclassified

Bifurkasi Pada Model Penyebaran Penyakit MERS-CoV di Dua Wilayah dengan Populasi Konstan

Owen

2022

Jambura J. Math

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Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is caused by a novel coronavirus and it can be a human-to-human transmission disease. World Health Organization (WHO) reported the disease outbreak first happened in Saudi Arabia in 2012 and the last case is reported in 2019. In 2018, MERS-CoV outbreaks were reported in the Republic of Korea, United Kingdom of Great Britain, Northern Ireland, Saudi Arabia, Uni Arab Emirates, Oman, and Malaysia. Cases that are identified outside the Middle East are usually caused by traveling people who were infected in the Middle East and then traveled back to their country. The previous research had constructed a mathematical model for the transmission of MERS-CoV in two areas by separating the human population into susceptible and infectious groups. It focused on the basic reproductive number and sensitivity analysis. In this paper, we simplify the model with the assumption that the total population of each area is constant. Using Lagrange Multiplier Method, we find some co-dimension one and co-dimension two bifurcations i.e.fold bifurcation and cusp bifurcation, respectively. We get the domain of parameters where three, two and one non-trivial equilibrium point occurs. We also find a transcritical bifurcation point such that the disease-free equilibrium point is stable on some parameter domains.

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“…Several mathematical models have investigated the dynamics of SARS-CoV-2 [7] , [11] , [25] , [38] , [39] , [40] and its strains [10] , [12] , [21] , [46] . Most of the multi-strain SARS-CoV-2 models do not capture randomness.…”

Section: Introductionmentioning

confidence: 99%

Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2

Omame

Abbas

Din

2023

Mathematics and Computers in Simulation

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Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV

Cited by 53 publications

References 36 publications

An optimal control model for COVID‐19, zika, dengue, and chikungunya co‐dynamics with reinfection

An optimal control model for COVID‐19, zika, dengue, and chikungunya co‐dynamics with reinfection

Bifurkasi Pada Model Penyebaran Penyakit MERS-CoV di Dua Wilayah dengan Populasi Konstan

Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2

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