Since 2020, Thailand has been impacted by the COVID-19 pandemic, which continues to persist into 2025. In response, the country has implemented various disease control measures, including public health campaigns and vaccination programs. While these strategies are still in place, they are now applied with less intensity, allowing people to return to a more normal way of life. However, this relaxed approach can contribute to continued disease transmission. In this study, we shift focus from conventional control measures-such as vaccination, mask-wearing, and social distancing-to strategies aimed at coexisting with the disease while minimizing its spread. Specifically, we investigate the impact of treating symptomatic and severe patients to reduce their infectiousness and thereby lower the risk of transmission to others. To achieve this, we develop a mathematical model of COVID-19 transmission dynamics and apply it using Thailand's 2025 data. We analyze the stability of both the disease-free and endemic equilibrium points and explore an optimal control problem related to medical treatment strategies. Our findings suggest that reducing the infectiousness of symptomatic and severe cases through effective treatment can help slow down the spread of COVID-19, supporting safer coexistence in a society returning to normalcy.

In this work, we develop a population dynamics model of Mycobacterium tuberculosis (Mtb), the bacteria responsible for tuberculosis (TB), to evaluate the impact of bacterial competition on infection prevalence. We consider two types of Mtb population growth: The first is caused by bacteria that grow inside each infected macrophage and is believed to be correlated with the number of infected macrophages; The second is that extracellular bacteria grow through self-replication. In this study, we modeled the immune response to Mtb bacterial infection in the lungs using a five-dimensional differential equation system. This model represents changes in the number of healthy macrophages, infected macrophages, activated macrophages cells, extracellular bacterial particles, and naive T cells. Qualitative analysis and numerical results reveal the existence of two equilibrium points: disease-free equilibrium and endemic equilibrium, which represent latent or active tuberculosis based on the number of bacteria. In addition, a sensitive analysis of the model parameters shows that macrophages are not sufficient to control the initial invasion of Mtb. The immune system must therefore employ more complex defense mechanisms to contain Mtb infection, such as recruiting various elements of immune system and forming granulomas.

The gravity model which is based on Newton’s gravitational law, has been widely used as a spatial interaction model in the past few decades. Spatial interactions are important in epidemic modeling as different populations in the world are interconnected by them. Human dispersal behaviors are spatial interactions and they are crucial aspects of infectious disease spread. However, many existing compartmental models model epidemics in a single area. Hence, a gravity model approach to model epidemics incorporated with a multipatch compartmental model is studied here. Both human dispersal behaviors within a patch and between patches are considered. When the human dispersal behaviors within a patch are modeled, the denominator of the general gravity model becomes zero. An alternative power-based distance decay function is introduced to the gravity model to address that research gap. The parameters of the modified gravity model are estimated using a hybrid method combining ordinary least squares (OLS) and nonlinear least squares (NLS) methods (Hybrid OLS-NLS method).

In this study, we propose a deterministic double dose vaccination model of COVID-19 transmission dynamics optimal control with cost-effectiveness analysis. It is imperative for decision-makers and the government to prioritize the application of preventive and control measures for COVID-19 based on efficiency and costbenefit analysis. This is pivotal in resource-constrained regions where the disease is endemic. Thus, this work is mainly devoted with the development and analysis of an optimal control for COVID-19 dynamics with five timevarying functions; first dose vaccination, second dose vaccination, personal protection, testing or screening, and treatment. The model is qualitatively analysed with the overall goal to minimize the spread of COVID-19 and the costs related to control implementation with the aid of optimal control theory. The effect of adopting each control intervention in each of the three distinct groups which are created by classifying all conceivable combinations of at least three control interventions is demonstrated through the numerical simulations of the optimality system. Using the average cost-effectiveness ratio and incremental cost-effectiveness ratio techniques, the most economical control intervention is determined for each group. The study reveals that when the resources are readily available, application of the strategy that combines optimal first dose vaccination, personal protection, screening or testing and treatment is as efficient as implementing all the five optimal control interventions simultaneously as they both avert the same number of infections. However, in resource-limited communities when joint implementation of only three interventions is possible, the strategy combining personal protection, testing or screening and treatment is strongly recommended. Out of all the intervention options being considered, this strategy is also affirmed to be the most cost-effective overall. Economic evaluation of the control intervention strategies further suggests that combination of first dose vaccination, second dose vaccination, testing or screening and treatment is the most cost-effective strategy when implementation of only four interventions is strictly allowed.

In this paper, a deterministic SIR plant mathematical model is proposed and analysed with the application of pesticides as a control measure. The primary purpose of this model is to study the role of pesticides in controlling disease prevalence in plant populations. The total plant population is subdivided into three categories: susceptible, infected, and recovered. Pesticides are considered to be applied to both susceptible and infected populations to prevent the spread of infection to unaffected plant populations. It is considered that plant populations can be recovered only through the use of pesticides. To ensure the biological validity and well-defined nature of the model, the positivity, boundedness, uniqueness and existence of solutions are analysed. The basic reproduction number (R0) of the infection is determined and observed that the disease-free equilibrium state is locally asymptotically stable whenever (R0) is less than unity and unstable otherwise. The sensitivity analysis of the basic reproduction number is carried out, and it is observed that the value of R0 decreases as the value of the death rate and the recovery rate of plants increases. Moreover, it is revealed that above a critical parameter value of the infective induce rate, the population starts oscillating periodically, and the endemic equilibrium state becomes unstable. Finally, numerical simulations are conducted in MATLAB software to compare the analytical findings. Overall, the results obtained from this analysis are both novel and significant, making them an intriguing and potentially valuable contribution to the field of theoretical ecology.

Trigona sp. is a stingless bee species that is widely distributed in tropical countries. It has castes in thecolony, i.e. queen, worker, and male bee. Despite its size, Trigona sp. can produce high-quality commoditiessuch as honey, propolis, and bee pollen. However, it is a vulnerable species since it’s pretty easy to be predatedby several predators and has a relatively short lifespan. In addition, there are still few mathematical studiesthat discuss the population dynamics of Trigona sp. Thus, in this study, we construct a mathematical modelof the Trigona sp. population in the form of a dynamical system. The model is a nine-dimensional non-lineardifferential equation that is constructed based on the stages in the bee population, namely the stages of eggs,larvae, and adult bees from each colony except the queen colony. Coexistence analysis, stability of equilibria, and also the death parameter sensitivity analysis are carried out in two scenarios. The first scenario is a situation where none of the workers die so that the food supply at the larval stage is sufficient. Meanwhile, the second scenario is a more common situation where some worker bees die from exhaustion resulting in an insufficient food supply for the larvae stage. Stable coexistence of all sub-structures and structural dependence on the foraging behavior of the workers are shown. All the results will be presented in numerical simulation. From the results of the coexistence and stability analysis, bee farmers can maintain food availability by increasing the number of workers in a colony, or providing food sources with high contains nectar and propolis at a relatively close distance to reduce the death of worker bees.

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.

COVID-19 is a viral disease that is caused by Severe Acute Respiratory Syndrome coronavirus 2 (SARSCoV-2) which has no approved vaccine. Based on the available non-pharmacological interventions like wearing of face masks, observing social distancing, and lockdown, this work assesses the impact of non-pharmaceutical control measures (social distancing and use of face-masks) and mass testing on the transmission of COVID-19 in Nigeria. A mathematical model for COVID-19 is formulated with intervention measures (observing social distancing and wearing of face masks) and mass testing. The basic reproduction number, R_0, is computed using next-generation method while the disease-free equilibrium is found to be locally and globally asymptotically stable when R_0< 1. The model is parameterized using Nigeria data on COVID-19 in Nigeria. The basic reproduction number is found to be less than unity (R_0 < 1) either when the compliance with intervention measures is moderate (50% <= alpha< 70%) and the testing rate per day is moderate (0,5 <=alpha_2 < 0,7) or when the compliance with intervention measures is strict (alpha>=70%) and the testing rate per day is poor (alpha_2 = 0,3). This implies that Nigeria will be able to halt the spread of COVID-19 under these two conditions. However, it will be easier to enforce strict compliance with intervention measures in the presence of poor testing rate due to the limited availability of testing facilities and manpower in Nigeria. Hence, this study advocates that Nigerian governments (Federal and States) should aim at achieving a testing rate of at least 0.3 per day while ensuring that all the citizens strictly comply with wearing face masks and observing social distancing in public.

We consider a SEIR model for the spread (transmission) of an infectious disease. The model has played an important role due to world pandemic disease spread cases. Our contributions in this paper are three folds. Our first contribution is to provide successive approximation and variational iteration methods to obtain analytical approximate solutions to the SEIR model. Our second contribution is to prove that for solving the SEIR model, the variational iteration and successive approximation methods are identical when we have some particular values of Lagrange multipliers in the variational iteration formulation. Third, we propose a new multistage-analytical method for solving the SEIR model. Computational experiments show that the successive approximation and variational iteration methods are accurate for small size of time domain. In contrast, our proposed multistage-analytical method is successful to solve the SEIR model very accurately for large size of time domain. Furthermore, the order of accuracy of the multistage-analytical method can be made higher simply by taking more number of successive iterations in the multistage evolution.

Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presented to describe the transmission of dengue. The equilibrium points and the basic reproduction number have been computed. The conditions which lead the disease free equilibrium and the endemic equilibrium have been determined. The local stability for the equilibrium points has been established based on the eigenvalues of the Jacobian matrix and the global stability has been analyzed by using the Lyapunov function theory. It is found that the stability of equilibrium points can be controlled by the reproduction number. In order to calculate the infection rate, data for infected human populations have been collected from several health institutions of Bangladesh. Numerical simulations of various compartments have been generated using MATLAB to investigate the influence of the key parameters for the transmission of the disease and to support the analytical results. The effect of treatment function over the infected compartment has been illustrated. The sensitivity of the reproduction number concerning the parameters of the model has been analyzed. Finally, the most sensitive parameter that has the highest effect over reproduction number has been identified.