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In a pandemic outbreak such as COVID-19, that spreads widely around the world requires in depth research to predict the pattern of its spread and strategies to reduce the number of spreads. Predictive control is a mathematical approach to control systems where a model is used to make predictions about the future behavior of a system, and these predictions are then used to determine the control actions that should be taken. Based on these predictions, control measures such as lockdowns and social distancing could be optimized to reduce the spread of the virus and minimize its impact. A dynamic model is needed for quick and precise handling decisions. Mathematical models Epidemiology can be used in various fields, the implementation of which is COVID-19. The presentation of a dynamical system can use the basic compartment model, in which critical 퐶 and death 풟 states are considered, addressing more possibilities of mutual transitions between compartment states. 풮ℰℐℛ풞풟 estimates and forecasts the COVID-19 spread under uncertainties and constraints. This paper focuses on This paper focuses on fit and predict the 풮ℰℐℛ풞풟 model with time dependent basic reproduction numbers and health resource-dependent death rates to real COVID-19 data in Indonesia. Data have been collected for a specific period of time, the best-fitting parameters have been obtained, and the changes in the basic reproduction number over time have been estimated. The presented model has included the transition probability of the infected state to the critical state and the transition probability of the critical state to the death state, based on different age groups, so that the number of hospital beds has also been cooperative in computing the compartment states. Using the best-fitting parameters of the 풮ℰℐℛ풞풟 model, the development of the compartment states in the near future was estimated. The simulation result shows that the obtained parameters of the 풮ℰℐℛ풞풟 model were reasonably satisfying where the simulated states from the model could fit the real data with a small degree of error so that it can be used to predict the path of further deployment. [ABSTRACT FROM AUTHOR]

Hoax is an information or explanation with unconfirmed truth. Nowadays, social media is the most used media in hoax propagation. If no action is taken, hoax propagation can cause serious problems. In this paper, a mathematical model representing social media hoax propagation with forgetting mechanism is analyzed in order to study the dynamics of social media hoax propagation in real life. Based on the analysis result, we obtain two equilibria, namely, non-endemic equilibrium and endemic equilibrium whose local stabilities depend on the basic reproduction number or R0. Social media hoax propagation occurs when R0 > 1 and does not occur when R0 < 1. Based on the sensitivity analysis result, the probability that a hoax is considered attractive and the forgetting rate of social media users against hoaxes are the most influential parameters on the dynamics of social media hoax propagation. Next, in order to minimize the number of hoax spreaders and hoax contents on social media, three control variables, namely, anti-hoax campaign, punishment for hoax spreaders, and hoax deletion by authorized parties, are imposed to the mathematical model. The optimal control problem in this paper is solved by using Pontryagin Maximum Principle. The numerical simulation result shows that the bundle implementation of three control strategies is the most effective scenario to minimize the number of hoax spreaders and hoax contents on social media. [ABSTRACT FROM AUTHOR]

COVID-19 disease is caused by a contagious family of corona virus. The dynamics of infectious novel virus SARS-Cov-2 is studied in this paper. We have studied a 7 class Susceptible-Exposed-Vaccinated-Asymptomatic Infected-Symptomatic Infected-Hospitalized-Recovered (SEVI1I2HR) model. Local stability for the equilibrium pointsis established with the help of Routh Hurwitz criterion. Proof of Global stability of the endemic equilibrium is done with Dulac's function. Numerical simulation carried out for the model suggests that minimizing the contact rate, hospitalization of the infected and vaccinations for all are the only ways to control the pandemic COVID-19. Sensitivity analysis of the considered parameters in the Basic Reproduction Number (R0) was performed to understand the most affected and sensitive parameters of the model. It was observed that R0 is directly proportional to the contact rate while inversely proportional to vaccination rate. [ABSTRACT FROM AUTHOR]

This paper introduces a mathematical model of SEIR for the spread of Ebola disease by appending one bat vector so that the model comes in as SEIR-SEI. We form a mathematical model into a non-linear differential equation system with seven dependent variables, and analyze a non-linear differential equations system to find the basic reproduction numbers and the equilibrium point of the system. Our study reveals that the stability analysis of the disease-free equilibrium is locally asymptotically stable if R0 < 1 and R1 < 1 so the infection will disappear from both human and bat populations. This paper also reveals the existence of endemic equilibrium points when R0 > 1. Numerical simulations are present to figure out the stability analysis of the endemic equilibrium points and to show that the numerical simulations are matching the model analysis. [ABSTRACT FROM AUTHOR]

In the present times, Covid-19 is a great concern for every country as it is spread in multiple countries across the globe. In this paper, we will try to estimate potential consequences of SARS-CoV-2 transmission through a compartmental model. As many parameters may be observed to predict about number of deaths and covid-19 cases due to SARS-Cov2. We will use SEIRD model to predict basic reproduction number with the help of collected data of confirmed Covid-19 cases, deaths and the clinical parameters. In the next part of paper, we will try to make forecast about the number of deaths in India. [ABSTRACT FROM AUTHOR]

Covid-19 is a severe pandemic with a high mortality rate caused by the infectious respiratory virus SARS-CoV-2. Viruses associated with respiratory tract infections will use epithelial cells and airway mucosa as initial targets and cause respiratory tract infections or organ damage. This paper develops a model for the spread of Covid-19 with the effect of vaccination and quarantine. This model has seven variables, namely Susceptible, Vaccinated, Exposed, Symptomatic, Asymptomatic, Quarantined, and Recovered. From this model, two equilibrium points are obtained, non-endemic and endemic equilibrium points. Further, we analyze the global stability using the Lyapunov method. If basic reproduction number (ℛ0) less than one, then the non-endemic equilibrium point is globally asymptotically stable, while if basic reproduction number more than one, then the endemic equilibrium point is globally asymptotically stable. Numerical simulations are given to describe the behavior of the spread of Covid-19 in Banten Province on February 1, 2022 until May 1, 2022 with the result that increasing vaccination rates can reduce susceptible subpopulations. From the simulation results, it is obtained with a value of ℛ0 = 0.0000103<1, meaning that the Covid-19 spread model is asymptotically stable at a non-endemic equilibrium point. This indicates that the spread Covid-19 will decrease over time. [ABSTRACT FROM AUTHOR]

In this paper, we study a susceptible-infectious-recovered (SIR) epidemic model with fuzzy parameters. We also consider vaccination and treatment as an effort to stop the spread of disease. The fuzziness in this model is due to the use of fuzzy sets to represent the rate of disease transmission, the increase in mortality due to disease, and the rate of treatment of infected individuals. Further, we find and analyze the stability of the equilibrium point, and determine the basic reproduction number using the next generation matrix approach. Finally, to illustrate the theoretical results, we apply the model to the data on the spread of Tuberculosis in Indonesia. We performed numerical simulations using the software R. [ABSTRACT FROM AUTHOR]

Japanese encephalitis (JE), a public health problem for the entire world, is caused by a virus called Japanese encephalitis virus (JEV) which is spread by mosquitoes. According to WHO's report, nearly 68000 clinical cases of JE are reported globally each year and approximately 13600 to 20400 are deaths. Here, a mathematical model of JE is formulated considering different control measures such as vaccination, treatment, insecticide and efforts to reduce environmental discharges. An explicit expression of basic reproduction number is formulated and the stability of disease-free and endemic equilibrium of the system is analyzed. In this paper, we have formulated an optimal control problem and analyzed different strategies considering the minimum cost for applying such strategies. We have investigated the results of fixed control for endemic equilibrium both numerically and graphically. We have solved the optimal problem numerically when control parameters are time-dependent by applying Runge-Kutta 4th order forward and backward method and presented graphically. In our present work, we discussed the best cost-effective control strategy to prevent Japanese encephalitis when we consider environmental discharges have a positive impact on the breeding of mosquitoes and the growth of the pig population. [ABSTRACT FROM AUTHOR]

This paper studies the dynamics of Ebola virus disease transmission using Susceptible-Exposed-Infected-Recovered (SEIR) model. The proposed SEIR model has been analysed in two equilibrium states, mainly the disease-free equilibrium and endemic equilibrium. The stability criteria of the equilibria have been studied using the Jacobian Linearization and Routh-Hurwitz criterion. Simulations of the proposed model have been performed using data from the Ebola cases in Guinea. The acquired results revealed that the basic reproduction number, R0 obtained is 1.51, indicating that the Ebola virus disease is going to cause an epidemic state in Guinea. The simulations performed using MATLAB showed that the number of infection cases decreased in less than 100 days. Apart from that, the different values of parameters were considered to analyse the R0 values and the dynamics of each compartment of the proposed SEIR model. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear mathematics model that is formulated and analyzed to assess the impacts of quarantine and intense medical intervention on the dynamics of Coronavirus Disease 2019 (COVID-19). An extended SEIR model with quarantine and the hospitalization compartment is proposed to simulate the COVID-19 spread. The model considers seven stages of infection: susceptible, exposed, asymptomatic, symptomatic, quarantined asymptomatic, hospitalized symptomatically, and recovered. A deterministic system of bilinear incidence nonlinear differential equations is used to model it. It was found that the model has two equilibrium points: the disease-free equilibrium point and the endemic equilibrium point. The next-generation matrix approach is used to calculate the basic reproduction numbers. The global asymptotical stability of the proposed model's equilibria is examined using the Lyapunov function and the LaSalle invariance principle. When the basic reproduction number is less than unity, the disease-free equilibrium point is globally stable, and when the basic reproduction number is more than unity, the endemic equilibrium point with a special case is globally stable, which takes the form of a deterministic system of nonlinear differential equations with bilinear incidence. Sensitivity analysis and numerical simulation results, using a reasonable set of parameter values. Finally, we investigate how the prevalence of COVID-19 is affected by the rates of transmission, quarantine, and hospitalization. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop the Coronavirus disease (COVID-19) transmission model using the fractional-order differential equation defined by Caputo. This model is developed based on the susceptible-exposed-infected-recovered model, commonly known as the SEIR model. The basic reproduction number, denoted by R0, is computed using the next-generation matrix method. The disease-free equilibrium point is evaluated, and local stability analysis is performed. The analysis shows that the disease-free equilibrium is locally asymptotically stable when R0<1 and unstable when R0>1. In other words, the COVID-19 disease can be eliminated when R0< 1. Finally, numerical results are presented based on the real data of COVID-19 cases in Malaysia. [ABSTRACT FROM AUTHOR]

Isolation and fumigation play an essential role in the mechanism of the spread of fowl pox disease. This paper establishes a mathematical model to describe the spread of fowl pox in chicken farms by considering two interventions; isolation intervention to reduce the spread of feathers containing the virus and fumigation intervention to kill fowl pox vectors of adult mosquitoes and their larvae. The model was constructed as a ten-dimensional non-linear ordinary differential equation. Furthermore, analytical and numerical studies were carried out on the constructed model to determine the existence and analyze the disease-free equilibrium point, endemic balance point, basic reproduction number (ℛ0), and understand the long-term and shortterm dynamics of the constructed model. Based on the carried out analytical and numerical studies, it was concluded that although fumigation and isolation were proven to minimize fowl pox disease, fumigation was more reliable for maximum results. [ABSTRACT FROM AUTHOR]

In the context of the COVID–19, a great deal of attention is attracted in studying the infectious disease from both academics and practitioners. One of the most powerful tools for simulating, analyzing and predicting the future epidemic development is the mathematical modelling. We adopted a fractional-order SEIR compartment model to investigate the disease underlying dynamics. The major aim of the present study is to propose an efficient algorithm to solve the coefficient identification inverse problem. The latter is formulated as a minimization problem for a quadratic cost functional, which is solved by a numerical optimization methods. The basic reproduction number and the economic impact of the epidemic are also discussed. Computational experiments with real-world data are provided to demonstrate the suggested algorithm properties. The paper is concluded with final remarks concerning the applicability of the approach and possible further research. [ABSTRACT FROM AUTHOR]

In this paper, we develop a mathematical model for disease transmission with multiple different level of susceptibilities for different subpopulations. We begin with three different level of susceptibilities and then generalize the results to n different susceptibility cases. We explore the dynamics of the model by showing the existence of its equilibrium point together with their respective stability analysis. We also show their stability behavior with the basic reproduction number and give the criteria for the minimum intervention level for the disease transmission. We observe the population dynamics of the model using numerical simulation. Numerical examples show that there is a trade-off among susceptibility level, the intrinsic growth rate, and the initial value of the subpopulation in determining the dynamics of the population. In the presence of a disease, the initial value affects the short-term population size, however in the long-term the most significant factor affecting the population size is the intrinsic growth rate. A susceptible subpopulation which initially is abundant, but has a higher susceptibility to the disease with a low intrinsict gowth, might be driven to extinction if we assume that the disease affect the pecundity of the subpopulation. [ABSTRACT FROM AUTHOR]

Cigarettes are one of the tobacco products that contain many chemicals that cause various types of diseases. In addition, cigarettes can also cause addiction and dependence for smokers. The purpose of this work is to analyze the equilibrium point of the mathematical model of the cessation of smoking behavior and the application of optimal control in the form of education (ul) and candy treatment (u2). Based on the analysis of the uncontrolled model, two equilibrium points were obtained, namely the non-endemic equilibrium point and the endemic equilibrium point. The local stability of the equilibrium point and the existence of the endemic equilibrium point depend on the basic reproduction number (R0). The non-endemic equilibrium point is asymptotically stable if fulfills two conditions, there are β Λ − η M 0 μ μ (2 μ + δ + d + γ) < 1 and R0 < 1, while the endemic equilibrium point is asymptotically stable if R0 > 1. In this paper, parameter sensitivity analysis will also be carried out to determine the most influential parameters on the model. From the results of sensitivity analysis, the most influential parameters are parameters β and η. Furthermore, the control variable problem in the model is determined using the Pontryagin Maximum Principle. The results of numerical simulations show that giving control in the form of education and candy treatment simultaneously provides effective results to minimize the individual population of smoking with minimal costs. [ABSTRACT FROM AUTHOR]

Noroviruses are a group of related viruses that are highly contagious. Norovirus is a food-borne disease member of a group of viruses called caliciviruses, known previously as Norwalk-like viruses. The human can be infected norovirus from an infected person, contaminated food or water, or by touching contaminated surfaces. In this paper, we propose a mathematical epidemic model to describe the dynamics of Norovirus infection in the human population from contaminated and its dynamics was developed. In this paper, we propose a mathematical epidemic model to describe the dynamics of Norovirus infection in human population from contaminated. We estimate the basic reproduction number to evaluate the magnitude of the outbreak and the effectiveness of the medical and/or behavioral therapies required for control. Norovirus is transmitted by contaminated food products even if the Norovirus bacteria population in the environment is very small. The Norovirus can effectively control by removing contaminated food products. [ABSTRACT FROM AUTHOR]

HIV/AIDS is an infectious disease caused by the infection of HIV (Human Immunodeficiency Virus) virus that decrease the immune system by attacking and damaging CD4 cells which are types of white blood cells (lymphocytes). The decreasing of immune system due to HIV virus then causes damage to AIDS (Acquired Immunodeficiency Syndrome). People with HIV virus infection can take an ARV (Anti Retroviral Therapy) treatment. ARV treatment is an effort that can be done to reduce the HIV viruses inside the body and can extend life time before the disease turn into AIDS. In this paper, a mathematical model of the spread of HIV/AIDS with education and treatment will be discussed. Furthermore, a numerical simulation and sensitivity analysis of basic reproductive numbers will be discussed to determine the parameters which havethe most effect on the spread of HIV/AIDS disease. In the mathematical model of the spread of HIV/AIDS with education and treatment, the most influential parameters is the rate of transmission of susceptible individuals caused by an undiagnosed HIV virus individual and the level of success of education given to susceptible individuals as an effort to prevent the spread of HIV viruses. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematics model is described and analyzed to assess the impacts of prevention, quarantine and surface disinfection strategies. The basic reproduction number without controls is computed. The application of Lyapunov's function is used to analyze the global asymptotical stability for the equilibria of the proposed model. We also provide an overview of optimal control issues and establish prerequisites for reducing exposed and infected populations while accounting for implementation costs. The existence of optimal controls and characterization is established using Pontryagin's Maximum Principle. The results of the numerical simulation show that there is a match with the results of the analysis. The numerical solution to the optimal control problem uses the forward-backward Sweep method which is implemented in the MATLAB program. The results of this study indicate that the application of a combination of all controls (prevention, quarantine, and surface disinfection) is an effective control strategy in reducing disease epidemics and implementing control costs. [ABSTRACT FROM AUTHOR]

COVID-19 is a disease caused by virus infection from coronavirus family called SARS-CoV-2. Due to its high transmission, COVID-19 is declared by WHO (World Health Organization) as a pandemic. In this paper we developed SEQIRD (Susceptible Exposed, Quarantined, Infected, Recovery, Deceased) model for the spread of COVID-19. We also analyzed the stability of the model. The analytical results show that there are two equilibrium points, endemic equilibrium point and non-endemic equilibrium point. The stability analysis of equilibrium points is determined by basic reproduction number (ℜ0) which is derived from Next Generation Matrix (NGM). The local stability of the system around the equilibrium point is determined by the Routh-Hurwitz stability criteria. The disease-free equilibrium point or non endemic equilibrium is asymptotically stable if the basic reproduction number is less than one (ℜ0 < 1) and the endemic equilibrium point is asymptotically stable if ℜ0 > 1. From the stability analysis, we obtained the reproduction number ℜ0 = 4.3, that is endemic locally asymptotically stable. The numerical simulation are also provided to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

Drug abuse was becoming a health and social problem around the world, including Indonesia. Some mathematicians have been working on mathematical model of drug abuse spreading. In this paper we will add a death rate by addiction on mathematical model that already established. On previous model, the death rate was only the natural death rate. By the fact we know that some drug user has been death because their addiction. After modifying the model, we do some analysis to find the equilibrium points and also find the basic reproduction number using Next Generating Matrix (NGM). Then we verify the local stability of the equilibria and do some simulation to give the illustration. The result showed that the death rate caused by addiction influence the dynamic of every compartment. [ABSTRACT FROM AUTHOR]

In this paper, the global stability analysis of the pertussis model with maternally derived immunity is studied. The model is qualitatively analysed to investigate the asymptotic behavior of the model with respect to the equilibria. Using the Lyapunov function method, the pertussis-free equilibrium is determined to be globally asymptotically stable when the associated basic reproduction number is less than unity. Furthermore, the study is also extended to prove the existence of a globally asymptotically stable pertussis endemic equilibrium using a suitable nonlinear Lyapunov function. [ABSTRACT FROM AUTHOR]

The deadly coronavirus continues to wreak havoc around the world, demanding the creation of mathematical models and computational models that could enhance worldwide efforts to identify important transmission characteristics. The SEIQR pandemic model will be used to develop a new approach to analyzing and managing the covid-19 outbreak.A mathematical model based on suitable non-linear differential equations is used to disseminate covid-19. The model parameters are determined by fitting the model with data from an actual pandemic scenario, and the model allows for COVID-19 (COV-19) infection to spread with compartment class isolation or quarantine. With appropriate assumptions, a sensitivity analysis is performed to determine the effect of a relationship between the dependent and independent variables. The reproduction number's local sensitivity has been investigated. The data is made particular by the model, which is mathematically fitted. The findings point to ways to prevent corona from spreading while maintaining contact and recovery rates. The basic reproduction number's elasticity as a measure of dynamical system control parameters is also investigated. Numerical simulations were also performed to demonstrate that the suggested model is accurate for the type and spread of the outbreak. [ABSTRACT FROM AUTHOR]

A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to a dataset from the UK. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically. [ABSTRACT FROM AUTHOR]

We study an SEIRS epidemiological model for the infectious disease Tuberculosis using differential equations. The entry of an infectious individual into a susceptible population leads to the spread of infection. There are chances of getting infected even after recovery, which has been taken into consideration. When the infection will establish itself or diminish is researched and validated by stability of equilibrium. The factor which gives the conclusion of equilibrium is the Basic Reproduction Number 퓡0. If 퓡0 < 1 then infection dies out and if 퓡0 > 1, the infection would establish itself. [ABSTRACT FROM AUTHOR]

Nowadays, the scientific community's considerable commitment in the research of social networks is it's link to disease propagation. The notion of social network have pulled in extensive premium and interest from the social and behavioral science community in late many years. The incidence of infectious diseases are becoming more and more alarming these days and the year 2019 marked the beginning of yet another episode of global pandemic, the COVID-19, novel corona virus infection. Covid-19 is spread via social networks, which are largely made up of social interactions. It is incredibly common to analyze the gradual transformation and dynamics of epidemiological ailments, which are disseminated via networks of interactions between individuals, using SN view point. Here, we are trying to understand the pandemic situation by looking in the lenses of SNA. The idea of basic reproduction number, six degree of separation and SIR Modelling are used. [ABSTRACT FROM AUTHOR]

A nonlinear cholera mathematical model is formulated and analyzed by incorporating awareness, vaccination and sanitation. Cholera is an infectious disease which is transmitted by water and food that has been contaminated by human waste. The existence of the equilibria and the stability of equilibria for the model are studied and investigated thoroughly. The basic reproduction number (R0) for simple cholera model is calculated. The disease-free equilibria (DFE) of the model is locally as well as globally asymptotically stable with some restriction on parameters, whenever R0 < 1. The endemic equilibria of the system exist and locally asymptotically stable with certain conditions, whenever R0 > 1. The sensitivity analysis is carried out to know the key parameters that affects the basic reproduction number that can be regulated in order to control the Cholera infections. Also, the numerical simulation is presented to support the analytical findings. [ABSTRACT FROM AUTHOR]

Pneumococcal pneumonia is a type of community-acquired pneumonia which is an acute respiratory infection caused by Streptococcus pneumoniae bacteria. In this study, a mathematical model on the spread of Pneumococcal pneumonia is constructed by considering vaccination and hospital care interventions. The model is formed by dividing the human population based on their health status. We consider several things in the model's construction, such as asymptomatic individuals, the latent phase during infection, and interventions of vaccination and hospitalization. Analytical studies are carried out to find and analyze the existence and local stability of the equilibrium points, determining the basic reproduction number (R0), and investigate the type of bifurcation of the model. We find that the model exhibits a forward bifurcation when R0 = 1. These result means that we have to reduce the value of R0 as large as possible using vaccination and/or hospitalization to avoid the existence of Pneumococcal pneumonia in the community. Several numerical experiments are shown to see the visualization of the model. The simulation results show that the rate of vaccination and the rate of hospitalization only have a very significant effect at the beginning in reducing the value of R0, but not as significant when the value of the two rates given is large enough. It is also concluded that an increase in the rate of vaccination is more successful in reducing the number of individuals infected with Pneumococcal pneumonia compared to an increase in the rate of hospitalization. Thus, it will be more effective for intervention in the field to rely on vaccination compared to hospitalization. The type of vaccine used in the vaccination process also has a significant effect in reducing the value of R0. This is because the elasticity value of the parameter ζ, which is the infection reduction value because the effectiveness of the vaccine, has the most significant effect in reducing the value of R0 compared to the parameters that indicate the rate of vaccination and the rate of hospitalization. [ABSTRACT FROM AUTHOR]

This research develops a mathematical model of the SIWR cholera disease model by adding two vectors: fly and fish. This research consisted of four populations: the individual populations, the bacterial populations in water, the fly vector populations, and the fish vector populations. Two equilibrium points are obtained from the mathematical model: the disease- free equilibrium point and the endemic equilibrium point. The disease-free equilibrium point is locally asymptotically stable if (R0 <1). If (R0 < 1) then the disease will disappear, and if (R0 > 1) then the disease becomes an epidemic. The numerical simulations figure the analyzed results with parameter values taken from several sources to support the stability analysis results. Sensitivity analysis results are analyzed to find which parameter is the most dominant to affect the disease's endemicity. The results revealed that the parameters ε (transmission of infected individuals to individuals removed) and β (the infective contact rate between susceptible individuals and water contaminated) in sequence showed the most dominant sensitivity index through the basic reproduction number. [ABSTRACT FROM AUTHOR]