Mathematical model for the control of infectious disease

Peter, Olumuyiwa James; Akinduko, O. B.; Oguntolu, Festus Abiodun; Ishola, C Y

doi:10.4314/jasem.v22i4.1

Cited by 7 publications

(8 citation statements)

References 5 publications

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“…However, after these few days, an inflexion point is reached and then the population begins to increase steadily for the remaining 100 days due to the loss of immunity of the recovered human population. This result is in agreement with the results of [20] and [6]. It can be observed that an increase in the contracting rate of the susceptible class via contact with the carrier class, , leads to a decrease in the population of this compartment.…”

Section: Numerical Simulations and Discussion Of Resultssupporting

confidence: 92%

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Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment

2019

MTM

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In this paper, a new mathematical model which takes into account the human and vector populations together with their interactions during Lassa fever disease transmission was developed. This transmission process is denoted by a seven mutually exclusive compartments for the human and vector populations. The proposed model is used to introduce the incubation period of the disease, a period in which an infected individual is yet to be symptomatic but infectious however, as denoted by the carrier human compartment. This carrier compartment was critically examined for its short and long term effects on the spread and control of the disease. Local and global stability analyses of the equilibrium points of the model was carried out using the first generation matrix approach and the direct Lyapunov method respectively. These analyses showed that the disease free equilibrium point of the developed model is locally asymptotically stable but not globally asymptotically stable. It was also observed that, although, there exist a unique endemic equilibria for the disease, this equilibria however is not stable. Numerical simulations of the model were carried out by implementing the MATLAB ODE45 algorithm for solving non-stiff ordinary differential equations. The results of these simulations are the effects of the various model parameters on each compartment of the developed model. Based on the findings of this research, necessary recommendations were made for the applications of the model to an endemic area.

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Section: Numerical Simulations and Discussion Of Resultssupporting

confidence: 92%

“…This result is in slight contrast with those in previous literatures. According to [3] and [20], the infected human compartment experiences a rapid increase between time 0 and 5. This increase was ascribed to the progression from the susceptible human population to the infected human population.…”

Section: Infected Human Populationmentioning

confidence: 99%

Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment

2019

MTM

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“…In 1927, W.O. Kermack and A.G. McKendrick proposed a complete mathematical model [15] to investigate the spread of infectious diseases by studying the Black Death that ravaged London in the 17th century and the plague that was prevalent in Mumbai in the early 20th century, and established an infectious disease warehouse model—the SIR infectious disease model [16] . Subsequently, numerous scientists studying epidemic diseases presented different models, in addition to the SIR model.…”

Section: Related Workmentioning

confidence: 99%

SQEIR: An epidemic virus spread analysis and prediction model

Sun²,

Lin³

2022

Computers and Electrical Engineering

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“…Coronavirus belong to a group of viruses that infect and causes diseases in human and other animals. It is thought that the virus might be of bat origin, and the transmission of the virus might be linked to a seafood market exposure named as Huanan Seafood Wholesale Market in Wuhan, where sold meat and live animals [22]. The World Health Organization (WHO), China Country Office discovered a case of pneumonia of unknown aetiology, first detected in Wuhan city, Hubei province in China on December 2019 [3] [23].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model of nonlinear differential equation for controlling global dynamics of coronavirus disease 2019 (COVID-19)

Vezhopalu

Sarma

2022

ijhs

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In this paper, we have introduced new mathematical model of Coronavirus Disease (COVID-19) Transmission Model as a system of six nonlinear differential equations to analyze the spread and control of this latest outbreak pandemic disease. This new mathematical model is analysed with the help of optimal control analysis. The main purpose of this optimal control theory which applied to the model is to show the existence of optimal controllers for the nonlinear dynamic system. Based on the assumptions, we also studied and formulate an optimal control model for a coronavirus disease dynamic system in terms of mathematical differential equations in order to focus the effects of prevention and control measures with minimal implementation cost. Then, we established the basic reproduction number , which makes possible to check whether a prominent infectious disease will continue to spread or not in a susceptible population. The paper was also extended to assess the conditions under which the population will be free of disease. In particular, we focus to include in the mathematical model, quarantine procedure applied to both the infected individuals and to the highly risk of total population, which is expected to be useful.

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Mathematical model for the control of infectious disease

Cited by 7 publications

References 5 publications

Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment

Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment

SQEIR: An epidemic virus spread analysis and prediction model

A mathematical model of nonlinear differential equation for controlling global dynamics of coronavirus disease 2019 (COVID-19)

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