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Abstract This study employs a mathematical model to analyze and forecast the severe outbreak of SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2), focusing on the socio-economic ramifications within the Thai population and among foreign tourists. Specifically, the model examines the impact of the disease on various population groups, including susceptible (S), exposed (E), infected (I), quarantined (Q), and recovered (R) individuals among tourists visiting the country. The stability theory of differential equations is utilized to validate the mathematical model. This involves assessing the stability of both the disease-free equilibrium and the endemic equilibrium using the basic reproduction number. Emphasis is placed on local stability, the positivity of solutions, and the invariant regions of solutions. Additionally, a sensitivity analysis of the model is conducted. The computation of the basic reproduction number (R0) reveals that the disease-free equilibrium is locally asymptotically stable when R0 is less than 1, whereas the endemic equilibrium is locally asymptotically stable when R0 exceeds 1. Notably, both equilibriums are globally asymptotically stable under the same conditions. Through numerical simulations, the study concludes that the outcome of COVID-19 is most sensitive to reductions in transmission rates. Furthermore, the sensitivity of the model to all parameters is thoroughly considered, informing strategies for disease control through various intervention measures.

The dengue viruses (of which there are four strains) are the causes of three illnesses of increasing severity; dengue fever (DF), dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS). Recently, dengue fever has reached epidemic proportion in several countries. Strategies or preventative methods have to be developed to combat these epidemics. This can be done by development of vaccines or by preventing the transmission of the virus. The latter approach could involve the use of mosquito nets or insecticide spraying. To determine which strategy would work, we test the strategy using mathematical modeling to simulate the effects of the strategy on the dynamics of the transmission. We have chosen the Susceptible-Exposed-Infected-Recovered (SEIR) model and the SusceptibleExposed-Infected (SEI) model to describe the human and mosquito populations, repectively. We use the Pontryagin's maximum principle to find the optimal control conditions. A sensitivity analysis revealed that the transmission rate $ ({\gamma }_{h}, {\gamma }_{v}) $, the birth rate of human population ($ {\mu }_{h} $), the constant recruitment rate of the vector population ($ A $) and the total human population ($ {N}_{h} $) are the most influential factors affecting the disease transmission. Numerical simulations show that the optimal controlled infective responses, when implemented, cause the convergence to zero to be faster than that in uncontrolled cases.

Cassava mosaic disease (CMD) is found in many countries around the world. This disease is caused by a mosaic virus carried by whitefly. It hurts the growth and yield of cassava, which in turn causes damage to farmers who grow cassava. In this paper, we present a model for the transmission of CMD dynamics by the ordinary differential equation system and recommend the optimal control for this model when controlling the disease by uprooting diseased cassava and spraying insecticides. For this model analysis, we are given the basic reproductive number R0, which is the threshold number for classifying the disease-free equilibrium point when R0 < 1 and the endemic equilibrium point when R0 > 1 by using the next-generation method. Disease-free equilibrium points and endemic equilibrium points have found conditions of stability. Sensitivity analysis of basic reproductive numbers reveals the impact of the parameters on disease outbreaks. Then, the model is modified to an optimal control problem with two optimal control parameters, in which the goal is to reduce cassava infections to a minimum. The necessary conditions for optimal control of disease were created by Pontryagin’s maximum principle. Numerical simulations are shown to demonstrate the effectiveness of the control system in the final section.

Cassava mosaic disease (CMD) is caused by a virus transmitted by the whitefly. This disease can destroy cassava at any stage of its growth and it resulted in lower cassava yields. In this paper, we developed a mathematical model for the epidemic of cassava mosaic disease with a deterministic model which has saturation incidence rates. This model aims to explain the effect of vectors on cassava disease outbreaks. First, this model was analyzed using standard dynamic methods to determine the behavior of the solution. We found the existence and condition of disease-free and endemic steady state. The basic reproductive number ($ R_0 $) is obtained by using the next-generation method which $ R_0 $ helps assess the ability to spread infectious diseases. Second, the stability of the steady state was analyzed, then we obtain the condition of existence of local stability and global stability at each steady state of this model. Third, analysis of the sensitivity indices in the threshold number to determine the effect of the various parameters. Finally, the results of the theoretical model were validated by numerical simulations. It is represented by various graphs converging at a steady state and stable.

The world has been fighting against the COVID-19 Coronavirus which seems to be constantly mutating. The present wave of COVID-19 illness is caused by the Omicron variant of the coronavirus. The vaccines against the five variants (α, β, γ, δ, and ω) have been quickly developed using mRNA technology. The efficacy of the vaccine developed for one of the strains is not the same as the efficacy of the vaccine developed for the other strains. In this study, a mathematical model of the spread of COVID-19 was made by considering asymptomatic population, symptomatic population, two infected populations and quarantined population. An analysis of basic reproduction numbers was made using the next-generation matrix method. Global asymptotic stability analysis was made using the Lyapunov theory to measure stability, showing an equilibrium point’s stability, and examining the model with the fact of COVID-19 spread in Thailand. Moreover, an analysis of the sensitivity values of the basic reproduction numbers was made to verify the parameters affecting the spread. It was found that the most common parameter affecting the spread was the initial number in the population. Optimal control problems and social distancing strategies in conjunction with mask-wearing and vaccination control strategies were determined to find strategies to give better control of the spread of disease. Lagrangian and Hamiltonian functions were employed to determine the objective function. Pontryagin’s maximum principle was employed to verify the existence of the optimal control. According to the study, the use of social distancing in conjunction with mask-wearing and vaccination control strategies was able to achieve optimal control rather than controlling just one or another.

Abstract Background Bangkok plays a central role in the commerce of Thailand. This study aimed to characterize the district-level spatial-temporal patterns of dengue in Thailand and explore if a dengue peak in Bangkok led the peaks of dengue in other Thai provinces. Methods Monthly dengue data at district level in Thailand from January 2004 to December 2017 were obtained and used to assess the spatial and seasonal patterns of dengue in Thailand. As our seasonal decomposition and cross-correlation analyses showed that dengue in Bangkok peaked in November, which was a few months after the dengue peak in most other provinces, we used a time-series generalized linear model to explore if there was another province in which the dengue case number was most predictive of dengue case numbers in other Thai provinces. Results The highest district-level annual dengue incidence rates (per 10,000) in the three time periods (i.e. 2004–2008, 2009–2013 and 2014–2017) were 58.08 (Samphanthawong), 85.93 (Mueang Krabi), and 66.60 (Mae Sariang), respectively. Dengue incidence rates in the western part of Northern Thailand, southern part of Central Thailand, southern part of Eastern Thailand, and Southern Thailand were higher than in other regions. Dengue in most districts of Thailand peaked in June, July or August, but dengue peaks in all districts of Bangkok occurred in November. The number of dengue cases in Nakhon Ratchasima was most predictive of the number of dengue cases in other provinces in Thailand by a one-month lag. Conclusions Our results suggest that the dengue peak in Bangkok did not lead the peaks of dengue in other Thai provinces. Future research exploring how changes in socio-ecological factors (e.g. road network and climate factors) in Nakhon Ratchasima have affected the transmission of dengue in Thailand might shed some new light on the prevention and control of dengue.

COVID-19 is the name of the new infectious disease which has reached the pandemic stage and is named after the coronavirus (COVs) which causes it. COV is a single-stranded RNA virus which in humans leads to respiratory tract symptoms which can lead to death in those with low immunities, particularly older people. In this study, a standard dynamic model for COVID-19 was proposed by comparing a simple model and the optimal control model to reduce the number of infected people and become a guideline to control the outbreak. Control strategies are the vaccination rate and vaccine-induced immunity. An analysis was performed to find an equilibrium point, the basic reproduction number (R0), and conditions that generate stability by using Lyapunov functions to prove the stability of the solution at the equilibrium point. Pontryagin’s maximum principle was used to find the optimal control condition. Moreover, sensitivity analysis of the parameters was performed to learn about the parameters that might affect the outbreak in order to be able to control the outbreak. According to the analysis, it is seen that the efficacy of vaccines (b) and the infection rate (βan,βsn,βav,βsv) will affect the increased (decreased) incidence of the outbreak. Numerical analyses were performed on the Omicron variant outbreak data collected from the Thailand Ministry of Health, whose analyses then indicated that the optimal control strategy could lead to planning management and policy setting to control the COVID-19 outbreak.

Abstract Dengue disease is found in tropical and subtropical regions around the world. Dengue virus is the cause of dengue fever, dengue hemorrhagic fever, and dengue shock syndrome. It consists of 4 serotypes: DEN-1, DEN-2, DEN-3, and DEN-4. There are two modes of transmission for dengue virus in mosquito: horizontal transmission and vertical transmission. The mosquito can be infected when it bites an infectious human by horizontal transmission, but there can also be vertical transmission through sexual contact with an infected mosquito. This research presents a control mechanism based on our previously developed dengue model with vertical transmission. The two policies, namely vaccination and insecticide administration (Policy 1) and isolation and insecticide administration (Policy 2) are considered. The use of Pontryargin’s maximum principle allowed necessary and optimality conditions, thus facilitating the optimal control to be developed. Numerical solutions of our control systems and the conclusions of our two policies are presented.

In this paper, a model for the transmission of respiratory syncytial virus (RSV) in a constant human population in which there exist super spreading infected individuals (who infect many people during a single encounter) is considered. It has been observed in the epidemiological data for the diseases caused by this virus that there are cases where some individuals are super-spreaders of the virus. We formulate a simply SEIrIsR (susceptible–exposed–regular infected–super-spreading infected–recovered) mathematical model to describe the dynamics of the transmission of this disease. The proposed model is analyzed using the standard stability method by using Routh-Hurwitz criteria. We obtain the basic reproductive number (R0) using the next generation method. We establish that when R0<1, the disease-free state is locally asymptotically stable and the disease endemic state is unstable. The reverse is true when R0>1, the disease endemic state becomes the locally asymptotically stable state and the disease-free state becomes unstable. It is also established that the two equilibrium states are globally asymptotically stable. The numerical simulations show how the dynamics of the disease change as values of the parameters in the SEIrIsR are varied.

The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease.

Hand, foot and mouth disease (HFMD) is a virulent disease most commonly found in East and Southeast Asia. Symptoms include ulcers or sores, inside or around the mouth. In this research, we formulate the dynamic model of HFMD by using the SEIQR model. We separated the infection episodes where there is a higher outbreak and a lower outbreak of the disease associated with regional residency, with the higher level of outbreak occurring in the urban region, and a lower outbreak level occurring in the rural region. We developed two different optimal control programs for the types of outbreaks. Optimal Control Policy 1 (OPC1) is limited to the use of treatment only, whereas Optimal Control Policy 2 (OPC2) includes vaccination along with the treatment. The Pontryagin’s maximum principle is used to establish the necessary and optimal conditions for the two policies. Numerical solutions are presented along with numerical sensitivity analyses of the required control efforts needed as the control parameters are changed. Results show that the time tmax required for the optimal control effort to stay at the maximum amount umax exhibits an intrinsic logarithmic relationship with respect to the control parameters.

Dengue fever is a disease that has spread all over the world, including Thailand. Dengue is caused by a virus and there are four distinct serotypes of the virus that cause dengue DENV-1, DENV-2, DENV-3, and DENV-4. The dengue viruses are transmitted by two species of the Aedes mosquitoes, the Aedes aegypti, and the Aedes albopictus. Currently, the dengue vaccine used in Thailand is chimeric yellow tetravalent dengue (CYD-TDV). This research presents optimal control which studies the vaccination only in individuals with a documented past dengue infection (seropositive), regardless of the serotypes of infection causing the initial infection by the disease. The analysis of dengue transmission model is used to establish the local asymptotically stabilities. The property of symmetry in the Lyapunov function an import role in achieving this global asymptotically stabilities. The optimal control systems are shown in numerical solutions and conclusions. The result shows that the control resulted in a significant reduction in the number of infected humans and infected vectors.

Dengue disease is caused by four serotypes of the dengue virus: DEN-1, DEN-2, DEN-3, and DEN-4. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV) is a vaccine currently used in Thailand. This research investigates what the optimal control is when only individuals having documented past dengue infection history are vaccinated. This is the present practice in Thailand and is the latest recommendation of the WHO. The model used is the Susceptible-Infected-Recovered (SIR) model in series configuration for the human population and the Susceptible-Infected (SI) model for the vector population. Both dynamical models for the two populations were recast as optimal control problems with two optimal control parameters. The analysis showed that the equilibrium states were locally asymptotically stable. The numerical solution of the control systems and conclusions are presented.

Competing Interests: The authors have declared that no competing interests exist.

The optimum formulation and ultrasonic condition for fabrication of cinnamon essential oil (CEO) nanoemulsion were determined using Response Surface Methodology (RSM). The CEO nanoemulsions were formed using an ultrasonic bath (43 kHz at power output of 210 W) and an ultrasonic probe (24 kHz at power of 400 W). Probe ultrasonication outperformed bath ultrasonication since it produced nanoemulsions with smaller droplet size, narrower size distribution as measured using polydispersity index (PDI), and higher viscosity. The influences of sonication time of 180.23-351.77 s, temperature of 4.82-45.18 °C, and Tween® 80 concentration of 1-3% w/w on the droplet size, PDI, and viscosity were investigated using RSM based on Box-Behnken design (BBD). The RSM revealed that the sonication time of 266 s, temperature of 4.82 °C, and Tween® 80 of 3% w/w produced the optimum CEO nanoemulsion with droplet size of 65.98 nm, PDI of 0.15, and viscosity of 1.67 mPa.s. Moreover, the optimum nanoemulsion had good stability in terms of droplet size and PDI when storing at 4, 30, and 45 °C for 90 days. The antifungal activity of the optimum CEO nanoemulsion was then investigated against Aspergillus niger, Rhizopus arrhizus, Penicillium sp., and Colletotrichum gloeosporioides in comparison to CEO coarse emulsion. The results showed that the CEO nanoemulsion had better antifungal activity than coarse emulsion of CEO., (Copyright © 2019 Elsevier B.V. All rights reserved.)

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness.

The SEIR (Susceptible-Exposed-Infected-Recovered) model is used to describe the transmission of dengue virus. The main contribution is determining the role of the rainfall in Thailand in the model. The transmission of dengue disease is assumed to depend on the nature of the rainfall in Thailand. We analyze the dynamic transmission of dengue disease. The stability of the solution of the model is analyzed. It is investigated by using the Routh-Hurwitz criteria. We find two equilibrium states: a disease-free state and an endemic equilibrium state. The basic reproductive number ( R 0 ) is obtained, which indicates the stability of each equilibrium state. Numerical results taking into account the rainfall are obtained and they are seen to correspond to the analytical results.

The respiratory disease caused by the Influenza A Virus is occurring worldwide. The transmission for new strain of the H1N1 Influenza A virus is studied by formulating a SEIQR (susceptible, exposed, infected, quarantine, and recovered) model to describe its spread. In the present model, we have assumed that a fraction of the infected population will die from the disease. This changes the mathematical equations governing the transmission. The effect of repetitive contact is also included in the model. Analysis of the model by using standard dynamical modeling method is given. Conditions for the stability of equilibrium state are given. Numerical solutions are presented for different values of parameters. It is found that increasing the amount of repetitive contacts leads to a decrease in the peak numbers of exposed and infectious humans. A stability analysis shows that the solutions are robust.

The risk of dengue virus infection to travelers visiting dengue fever endemic regions was studied through the use of mathematical modeling. A Susceptible-Infected-Recovered (SIR) model is used to describe the transmission of dengue fever (DF) in an endemic region into which tourists enter. The dynamics of a new class of human, the traveler, is incorporated into the systems of first order differential equations in the SIR describing the dynamics of the transmission in the host region. Using standard dynamic analysis methods, the numbers of travelers who become infected with the dengue virus are calculated as a function of the length of time the tourist stays in the region.

The age profiles of the infected populations of two dengue hemorrhagic fever (DHF) epidemics, the 1997 epidemic, in Santiago de Cuba and the 1998 epidemic in Thailand, are compared. Using an age-structured model of disease transmission, the dependence of the forces of infection on age was determined for each epidemic. The difference in the behavior of the two epidemics and the role of primary and secondary infection in the development of DHF are discussed.

The influence of age structure in the susceptible class of the Susceptible-Infected Recovered (SIR) model used to describe the transmission of dengue hemorrhagic fever (DHF) was studied. This was done by first dividing all of the population classes into cohorts and then writing a set of coupled SIR equations for each cohort. The consequences of assuming different behavior of the transmission rates on the age structure in the DHF incidence rates were determined. In order for the predicted incidence rates to be similar to the DHF incidence patterns observed in several provinces in Thailand during the DHF epidemic in 1998, the transmission rates should be age dependent.