Qualitative Analysis of a Dengue Fever Model

Gbadamosi, Bolanle; Ojo, Mayowa M.; Oke, Segun Isaac; Matadi, Maba Boniface

doi:10.3390/mca23030033

Cited by 14 publications

(19 citation statements)

References 20 publications

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“…From above, the region ∇ is positively-invariant under models ( 10)- (11). Then the system is both epidemiologically and mathematically well-posed.…”

Section: Model Of Fractional Typementioning

confidence: 90%

“…Doing this will help reduce the severity of following Coronavirus outbreaks. There have been many proposed mathematical models and analysis by a large number of infectious disease researchers on COVID-19, and similar diseases see [2,3,4,5,6,7,8,9,10,11]. However, COVID-19 is rare, complex and many things are yet unknown, which set limitations to what known models could capture.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Iyiola¹,

Oduro²,

Zabilowicz³

et al. 2021

Preprint

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The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalization and deaths have been observed, and thousands of cases daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to understand the transmission of the disease better. Nonlocality involved in the model has made fractional differential equations appropriate for modeling the behavior. However, solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate (from exposed quarantine and recovered to susceptible and infected quarantined individuals), quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium analysis, and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam-Bashforth-Moulton method developed for the fractional order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19, especially quarantining exposed and infected individuals and the effective contact rate. Based on the results with different fractional order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is what is happening right now in many countries.

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“…From above, the region ∇ is positively-invariant under models ( 10)- (11). Then the system is both epidemiologically and mathematically well-posed.…”

Section: Model Of Fractional Typementioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Iyiola¹,

Oduro²,

Zabilowicz³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…To this end, we shall assume that the transmission rate of COVID-19 reduces, as function of good hygiene. Also, the form of this function is not too clear; however, we shall adopt the linear function here as used in [28] , [29] . Consequently, the transmission rate of the disease denoted by β ( H ) where H is the sanitation level is defined as a linear function of H as follows:

…”

Section: Model Formulationmentioning

confidence: 99%

Dynamic model of COVID-19 disease with exploratory data analysis

et al. 2020

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Novel Coronavirus is a highly infectious disease, with over one million confirmed cases and thousands of deaths recorded. The disease has become pandemic, affecting almost all nations of the world, and has caused enormous economic, social and psychological burden on countries. Hygiene and educational campaign programmes have been identified to be potent public health interventions that can curtail the spread of the highly infectious disease. In order to verify this claim quantitatively, we propose and analyze a non-linear mathematical model to investigate the effect of healthy sanitation and awareness on the transmission dynamics of Coronavirus disease (COVID-19) prevalence. Rigorous stability analysis of the model equilibrium points was performed to ascertain the basic reproduction number R 0 , a threshold that determines whether or not a disease dies out of the population. Our model assumes that education on the disease transmission and prevention induce behavioral changes in individuals to imbibe good hygiene, thereby reducing the basic reproduction number and disease burden. Numerical simulations are carried out using real life data to support the analytic results.

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“…Doing this will help reduce the severity of next coronavirus outbreaks. There have been many proposed mathematical models and analyses by a large number of infectious disease researchers on COVID-19 and similar diseases see [2][3][4][5][6][7][8][9][10][11]. Furthermore, some authors have proposed a SIR or related models for COVID- 19.…”

Section: Introductionmentioning

confidence: 99%

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

et al. 2021

View full text Add to dashboard Cite

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

show abstract

Qualitative Analysis of a Dengue Fever Model

Cited by 14 publications

References 20 publications

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Dynamic model of COVID-19 disease with exploratory data analysis

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

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