Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease

Nana-Kyere, Sacrifice; Banon, Desmond Titus; Marmah, Seth N.; Kwarteng, Daniel

doi:10.9734/jamcs/2019/v31i330113

Cited by 4 publications

(7 citation statements)

References 23 publications

(28 reference statements)

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“…This means that all the parameters can be identified by collecting data from this region during the process of parameter estimation. The parameter which describes the birth rate is most sensitive in the compartments , and , but with small magnitude and it is sensitive in in time interval [14][15][16][17][18][19] years. The sensitivities of the parameters and in model shows that these two parameters are more or less sensitive for any output or or or together.…”

Section: Discussionmentioning

confidence: 99%

“…Let , , , denote the corresponding numbers of individuals at time , without ambiguity; if they are abbreviated by , , , , respectively, then the model is presented by the following system of four non-linear Ordinary Differential Equations(ODEs) [14]:…”

Section: The Seir Model Of Hepatitis Bmentioning

confidence: 99%

“…The parameters used in the model are described in the Table 1 along with their assumed values [13][14] which we shall use to solve the model numerically in our onward course of work:…”

Section: The Seir Model Of Hepatitis Bmentioning

confidence: 99%

“…. We take the values of parameters as shown in the Table 1 and the initial conditions , , and , [14] for Model (1). We then develop the ODEs system of the sensitivity equations in accordance with Equation (5) for our model.…”

Section: Numerical Implementationmentioning

confidence: 99%

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Studying the Transmission of Hepatitis-B Virus Through Sensitivity Analysis

Ali

Munir²,

Hussain

et al. 2020

J. Sci. Arts

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This paper presents the sensitivity analysis of an epidemiological model, SEIR, describing the transmission of Hepatitis B Virus. The classical sensitivities, the system sensitivity and the sensitivity norms of the model have been found. The sensitivities show that the susceptible individuals are majorly affected by the birth rate, contact rate, the rate at which the exposed individuals become infected and the fraction of the infected individuals in the population. System sensitivity describes the sensitivity of the whole model output with respect to all the parameters. The results of the classical sensitivities of the parameters are in agreement with the results given by the system sensitivities. The contact rate, β has the largest sensitivity norm and the exposed infected fraction of the population, t_1 has the least sensitivity norm. The qualitative and the quantitative sensitivity studies of the SEIR model reaffirm each other.

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Section: Discussionmentioning

confidence: 99%

Section: The Seir Model Of Hepatitis Bmentioning

confidence: 99%

“…The parameters used in the model are described in the Table 1 along with their assumed values [13][14] which we shall use to solve the model numerically in our onward course of work:…”

Section: The Seir Model Of Hepatitis Bmentioning

confidence: 99%

Section: Numerical Implementationmentioning

confidence: 99%

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Studying the Transmission of Hepatitis-B Virus Through Sensitivity Analysis

Ali

Munir²,

Hussain

et al. 2020

J. Sci. Arts

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“…The exposed population comprises of those individuals who are infected but not yet infectious i.e., they are not capable of transmitting virus. This shows that the transmission rate of the HBV disease is assumed to be the contact rate between the susceptible and the infective [9]. The exposed class grows with the incidence rate + ⁄ but decreases due to the natural death rate of μ, due to transfer to with a rate , and due to transfer to with a rate .…”

Section: Model Assumptionsmentioning

confidence: 99%

Modified Model and Stability Analysis of the Spread of Hepatitis B Virus Disease

Desta¹

2019

AJAM

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In this study the infected population is classified into two categories viz., chronic and acute and thus developed a five compartmental SEI C I A R model. Also, both vaccination and treatments are included and studied their impact on the spread of hepatitis B virus. The present model is biologically meaningful and mathematically well posed since the solutions are proved to be positive as well as bounded. The basic reproduction number R O of the model is derived using the next generation matrix method. Further, the equilibrium points of the model are identified and mathematical analysis pertaining to their stability is conducted using Routh-Hurtiz criteria. It is shown that the disease free equilibrium point is locally and globally stable If R O ＜1. On the other hand, the endemic equilibrium point is proved to be stable if R O ＞1. Also, the numerical simulation study of the model is carried out using ode45 of MATLAB: Rung-Kutta order four. It is observed that, if the vaccination and treatment rates are increased then the infective population size decreases and evenfall to zero over time. Hence, it is concluded that the use of vaccination and treatment at the highest possible rates is essential so as to control the spread hepatitis B virus.

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