scholarly journals Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 703
Author(s):  
Meghadri Das ◽  
Guruprasad Samanta ◽  
Manuel De la Sen
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Reproduction Number ◽  
Psychological Treatment ◽  
Transmission Model ◽  
Uniqueness Criterion ◽  
Synthetic Drugs ◽  
The Basic Reproduction Number ◽  
Positivity And Boundedness

In this work, a fractional-order synthetic drugs transmission model with psychological addicts has been proposed along with psychological treatment. The effects of synthetic drugs are deadly and sometimes even violent. We have studied the local and global stability of the model with different criterion. The existence and uniqueness criterion along with positivity and boundedness of the solutions have also been established. The local and global stabilities are decided by the basic reproduction number R0. We have also analyzed the sensitivity of parameters. An optimal control problem has been formulated by controlling psychological addiction and analyzed by the help of Pontryagin maximum principle. These results are verified by numerical simulations.

scholarly journals The effects of non-pharmaceutical interventions on SARS-CoV-2 transmission in different socioeconomic populations in Kuwait: a modeling study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Fatima Khadadah ◽  
Abdullah A. Al-Shammari ◽  
Ahmad Alhashemi ◽  
Dari Alhuwail ◽  
Bader Al-Saif ◽  
...  
Keyword(s):  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Model ◽  
Socioeconomic Groups ◽  
Before And After ◽  
Cross Transmission ◽  
Community Transmission ◽  
The Impact ◽  
Pharmaceutical Interventions ◽  
The Basic Reproduction Number

Abstract Background Aggressive non-pharmaceutical interventions (NPIs) may reduce transmission of SARS-CoV-2. The extent to which these interventions are successful in stopping the spread have not been characterized in countries with distinct socioeconomic groups. We compared the effects of a partial lockdown on disease transmission among Kuwaitis (P1) and non-Kuwaitis (P2) living in Kuwait. Methods We fit a modified metapopulation SEIR transmission model to reported cases stratified by two groups to estimate the impact of a partial lockdown on the effective reproduction number ($$ {\mathcal{R}}_e $$ R e ). We estimated the basic reproduction number ($$ {\mathcal{R}}_0 $$ R 0 ) for the transmission in each group and simulated the potential trajectories of an outbreak from the first recorded case of community transmission until 12 days after the partial lockdown. We estimated $$ {\mathcal{R}}_e $$ R e values of both groups before and after the partial curfew, simulated the effect of these values on the epidemic curves and explored a range of cross-transmission scenarios. Results We estimate $$ {\mathcal{R}}_e $$ R e at 1·08 (95% CI: 1·00–1·26) for P1 and 2·36 (2·03–2·71) for P2. On March 22nd, $$ {\mathcal{R}}_e $$ R e for P1 and P2 are estimated at 1·19 (1·04–1·34) and 1·75 (1·26–2·11) respectively. After the partial curfew had taken effect, $$ {\mathcal{R}}_e $$ R e for P1 dropped modestly to 1·05 (0·82–1·26) but almost doubled for P2 to 2·89 (2·30–3·70). Our simulated epidemic trajectories show that the partial curfew measure greatly reduced and delayed the height of the peak in P1, yet significantly elevated and hastened the peak in P2. Modest cross-transmission between P1 and P2 greatly elevated the height of the peak in P1 and brought it forward in time closer to the peak of P2. Conclusion Our results indicate and quantify how the same lockdown intervention can accentuate disease transmission in some subpopulations while potentially controlling it in others. Any such control may further become compromised in the presence of cross-transmission between subpopulations. Future interventions and policies need to be sensitive to socioeconomic and health disparities.

scholarly journals Mathematical Analysis of an Immune-structured Hikungunya Transmission Model

2019 ◽  
Vol 12 (4) ◽  
pp. 1533-1552
Author(s):  
Kambire Famane ◽  
Gouba Elisée ◽  
Tao Sadou ◽  
Blaise Some
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Transmission Model ◽  
Acquired Immunity ◽  
Local Asymptotic Stability ◽  
Well Posed ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, itappears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the diseasefree equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

scholarly journals Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control

2021 ◽  
Vol 9 (1) ◽  
pp. 198-212
Author(s):  
Cheryl Q. Mentuda
Keyword(s):  
Optimal Control ◽  
Vector Control ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Model Comparison ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Transmitted Disease ◽  
The Basic Reproduction Number

Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.

scholarly journals Global dynamics of a Huanglongbing model with a periodic latent period

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yan Hong ◽  
Xiuxiang Liu ◽  
Xiao Yu
Keyword(s):  
Reproduction Number ◽  
Threshold Value ◽  
Transmission Model ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Temperature Dependent ◽  
Candidatus Liberibacter ◽  
Effects Of Temperature ◽  
Disease Free ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>Huanglongbing (HLB) is a disease of citrus that caused by phloem-restricted bacteria of the Candidatus Liberibacter group. In this paper, we present a HLB transmission model to investigate the effects of temperature-dependent latent periods and seasonality on the spread of HLB. We first establish disease free dynamics in terms of a threshold value <inline-formula><tex-math id="M1">\begin{document}$ R^p_0 $\end{document}</tex-math></inline-formula>, and then introduce the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> and show the threshold dynamics of HLB with respect to <inline-formula><tex-math id="M3">\begin{document}$ R^p $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Numerical simulations are further provided to illustrate our analytic results.</p>

scholarly journals A Fractional Order Dengue Fever Model in the Context of Protected Travellers

2021 ◽  
Author(s):  
E. Bonyah ◽  
M. L. Juga ◽  
C. W. Chukwu ◽  
Fatmawati
Keyword(s):  
Dengue Fever ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Climate Changes ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Qualitative Information ◽  
Uniqueness Of Solutions ◽  
Vector Borne Diseases ◽  
Vector Borne

AbstractClimate changes are affecting the control of many vector-borne diseases, particularly in Africa. In this work, a dengue fever model with protected travellers is formulated. Caputo-Fabrizio operator is utilized to obtain some qualitative information about the disease. The basic properties and the reproduction number is studied. The two steady states are determined and the local stability of the states are found to be asymptotically stable. The fixed pointed theory is made use to obtain the existence and uniqueness of solutions of the model. The numerical simulation suggests that the fractional-order affects the dynamics of dengue fever.

scholarly journals Stability and optimal control in a mathematical model of online game addiction

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5691-5711 ◽  
Author(s):  
Tingting Li ◽  
Youming Guo
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Control Strategy ◽  
Reproduction Number ◽  
Direct Transfer ◽  
Online Game ◽  
Optimal Control Strategy ◽  
Game Addiction ◽  
The Basic Reproduction Number

In this paper, we construct an online game addiction model(including susceptible, infective, professional and quitting compartments). We also consider that the direct transfer from the susceptible individuals to the professional individuals. Some properties of the model are derived by the basic reproduction number R0 and stability of all kinds of equilibria is obtained. Then we use Pontriagin?s maximum principle to solve the optimal control strategy. Finally, Numerical simulations are also conducted in the analytic results.

scholarly journals Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model

2021 ◽  
Vol 4 (1) ◽  
pp. 46-64
Author(s):  
Muhammad Afief Balya ◽  
Bunga Oktaviani Dewi ◽  
Faza Indah Lestari ◽  
Gayatri Ratu ◽  
Hanna Rosuliyana ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Rapid Test ◽  
Social Awareness ◽  
Transmission Model ◽  
Media Campaign ◽  
Single Intervention ◽  
The Impact ◽  
The Basic Reproduction Number

In this article, we propose and analyze a mathematical model of COVID-19 transmission among a closed population, with social awareness and rapid test intervention as the control variables. For this, we have constructed the model using a compartmental system of the ordinary differential equations. Dynamical analysis regarding the existence and local stability of equilibrium points is conducted rigorously. Our analysis shows that COVID-19 will disappear from the population if the basic reproduction number is less than one, and persist if the basic reproduction number is greater than one. In addition, we have shown a trans-critical bifurcation phenomenon based on our proposed model when the basic reproduction number equals one. From the elasticity analysis, we have observed that rapid testing is more promising in reducing the basic reproduction number as compared to a media campaign to improve social awareness on COVID-19. Using the Pontryagin Maximum Principle (PMP), the characterization of our optimal control problem is derived analytically and solved numerically using the forward-backward iterative algorithm. Our cost-effectiveness analysis shows that using rapid test and media campaigns partially are the best intervention strategy to reduce the number of infected humans with the minimum cost of intervention. If the intervention is to be implemented as a single intervention, then using solely the rapid test is a more promising and low-cost option in reducing the number of infected individuals vis-a-vis a media campaign to increase social awareness as a single intervention.

scholarly journals COVID-19 disease transmission model considering direct and indirect transmission

2020 ◽  
Vol 202 ◽  
pp. 12008
Author(s):  
Dipo Aldila
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Model ◽  
Indirect Transmission ◽  
Variation Of Parameters ◽  
The Media ◽  
Disease Transmission Model ◽  
The Basic Reproduction Number

A mathematical model for understanding the COVID-19 transmission mechanism proposed in this article considering two important factors: the path of transmission (direct-indirect) and human awareness. Mathematical model constructed using a four-dimensional ordinary differential equation. We find that the Covid-19 free state is locally asymptotically stable if the basic reproduction number is less than one, and unstable otherwise. Unique endemic states occur when the basic reproduction number is larger than one. From sensitivity analysis on the basic reproduction number, we find that the media campaign succeeds in suppressing the endemicity of COVID-19. Some numerical experiments conducted to show the dynamic of our model respect to the variation of parameters value.

OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS

2020 ◽  
Vol 28 (02) ◽  
pp. 351-376 ◽  
Author(s):  
MUHAMMAD ALTAF KHAN ◽  
SYED AZHAR ALI SHAH ◽  
SAIF ULLAH ◽  
KAZEEM OARE OKOSUN ◽  
MUHAMMAD FAROOQ
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Control Measures ◽  
Hepatitis B Infection ◽  
Control Variables ◽  
Effect Of Treatment ◽  
The Basic Reproduction Number

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction number and to investigate basic properties of the model such as the existence and stability of equilibria. In the absence of control measures, we prove that the disease free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. Also, using persistent theorem, it is shown that the infection is uniformly persistent, whenever the basic reproduction number is greater than unity. Using optimal control theory, we incorporate into the model three time-dependent control variables and investigate the conditions required to curtail the spread of the disease. Finally, to illustrate the effectiveness of each of the control strategies on disease control and eradication, we perform numerical simulations. Based on the numerical results, we found that the first two strategies (treatment and isolation strategy) and (vaccination and isolation strategy) are not very effective as a long term control or eradication strategy for HBV. Hence, we recommend that in order to effectively control the disease, all the control measures (isolation, vaccination and treatment) must be implemented at the same time.

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