Effect of awareness program on diabetes mellitus: deterministic and stochastic approach

Mollah, Saddam; Biswas, Santosh

doi:10.1007/s12190-020-01424-6

Cited by 6 publications

(6 citation statements)

References 44 publications

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“…Now researchers have been formulating mathematical models on diabetes mellitus to simulate, analyze, and understand the dynamics of diabetes. Earlier Mollah et al [24] formulated mathematical models under deterministic as well as the stochastic environment and tried to investigate the dynamics of diabetes mellitus under the effect of awareness. Their results reflect that awareness can prevent diabetes mellitus in the community.…”

Section: Discussionmentioning

confidence: 99%

“…Diabetes mellitus is not an infectious disease and not transmitted from human to human. So, we have taken β is the incident rate of unaware susceptible to diabetes complication and ββ 1 (0 < β 1 < 1) is the lower incident rate of aware susceptible to T2 diabetes complication [24].…”

Section: Model Formulationmentioning

confidence: 99%

“…Okosun et al studied the effect of treatment and surveillance of unaware infective on the HIV/AIDS epidemic outbreak by using the fundamental function of optimal control theory [20]. Some research articles have been published so far to explore the dynamics of diabetes of mathematical models by utilizing various factors [21][22][23][24]. Makanda provided a mathematical model for the impact of drug non-adherence on diabetes management [21].…”

Section: Introductionmentioning

confidence: 99%

“…They showed that T2 diabetes patients are more likely to get covid-19 if they have come into touch with covid-19 infected individuals [22]. Mollah et al developed mathematical models by considering the effect of awareness of diabetes mellitus in the general population in both deterministic and stochastic environments [24]. Their finding showed that awareness program on the population may reduce the diabetes mellitus.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Mollah

Biswas

2022

Int. J. Dynam. Control

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T2 diabetes is a silent killer and serious public health issue across the world, though awareness of diabetes allows understanding of the causes and prevention of the disease. With this inspiration, we formulate a deterministic model by incorporating awareness and saturated treatment function of the T2 diabetes model to study the dynamics of the disease. We have carried out thoroughly analysis of the model system, including positivity of solutions, boundedness, equilibrium, and stability analysis. Again, we consider the deterministic model system as an optimal control problem by taking awareness (M) and treatment (u) as time-depended control parameters. The sufficient conditions for optimal control for T2 diabetes are obtained utilizing the Pontryagin's maximum principle in time-dependent controls to find optimal strategies for disease control. We intended to assess the efficacy and costs of several strategies to determine which is the best cost-effective strategy with the limited resources for treatment. The parameters incident rate (β), awareness coefficient ( p), media (M), and treatment (u) highly influence the dynamics of T2 diabetes. Numerical simulations suggest that both awareness and treatment controls have a significant impact on the optimal system and are economically feasible to reduce the prevalence of T2 diabetes.

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Section: Discussionmentioning

confidence: 99%

Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Mollah

Biswas

2022

Int. J. Dynam. Control

Self Cite

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“…On the other hand, in mathematical modeling, there is a lack of research focus on studies dealing with co-infection of diabetes and COVID-19. Although, many mathematical models have been derived to understand the patterns of each disease (COVID-19 [33,34,35,36,37] and diabetes [38,39,40,41,42]), as of now only one study [43] has explored diabetes and COVID-19 co-infection. This paper [43] emphasizes that the negative impact of quarantine and several strategies to the lifting of the quarantine.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling Co-existence of Diabetes and COVID-19 : Deterministic and Stochastic Approach

Anusha

Athithan

2021

Preprint

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Diabetes affects the epidemiology of COVID-19 (Coronavirus Disease 2019), is correlated with the exorbitant threat of COVID-19 incidence and failure of treatment. Hence, studying the mechanisms behind the coexistence of diabetes and COVID-19 is useful for the development of better public health policies. In this article, we have developed a novel deterministic model for the co-infection of diabetes and COVID-19. It consists of five compartments corresponding to five population classes, namely, diabetes susceptible, diabetes patients, COVID-19 susceptible, COVID-19 infected and COVID19 recovered class. We have discussed the non-negativity and invariant region of the system. Next, the existence of equilibrium points and stabilities of different equilibria of the model are studied. Also, by using the next-generation matrix method the basic reproduction number (R0) is calculated. Further, we perform the sensitivity analysis of R0 and observed that reduction of transmission coefficient (α₁) from diabetes susceptible class to diabetes class is the most critical factor to control the co-infection. We endeavor to fit our model with the data given by the World Health Organization(WHO)[1] and it suits well with the data. Moreover, the deterministic model is extended into the stochastic model. And by using numerical simulations our results of stochastic and deterministic models are compared. Our numerical findings are performed through computer simulation, which illustrates the robustness of our model from the eco-epidemiological perspective. The results obtained highlight the burden of diabetes and COVID-19 coinfection and the role of the α₁ in the severity of the disease.

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Impact of awareness program on diabetes mellitus described by fractional-order model solving by homotopy analysis method

2022

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Effect of awareness program on diabetes mellitus: deterministic and stochastic approach

Cited by 6 publications

References 44 publications

Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Mathematical Modelling Co-existence of Diabetes and COVID-19 : Deterministic and Stochastic Approach

Impact of awareness program on diabetes mellitus described by fractional-order model solving by homotopy analysis method

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