A dynamic model for infectious diseases: The role of vaccination and treatment

Mathematical model for understanding the relationship between diabetes and novel coronavirus

A new model is proposed to explore interactions between diabetes and novel coronavirus. The model accounted for both the omicron variant and variants varying from omicron. The model investigated compartments such as hospitalization, diabetes, co-infection, omicron variant, and quarantine. Additionally, the impact of different vaccination doses is assessed. Sensitivity analysis is carried out to determine disease prevalence and control options, emphasizing the significance of knowing epidemics and their characteristics. The model is validated using actual data from Japan. The parameters are fitted with the help of "Least Square Curve Fitting" method to describe the dynamic behavior of the proposed model. Simulation results and theoretical findings demonstrate the dynamic behavior of novel coronavirus and diabetes mellitus (DM). Biological illustrations that illustrate impact of model parameters are evaluated. Furthermore, effect of vaccine efficacy and vaccination rates for the vaccine's first, second, and booster doses is conducted. The impact of various preventive measures, such as hospitalization rate, quarantine or self-isolation rate, vaccine dose-1, dose-2, and booster dose, is considered for diabetic individuals in contact with symptomatic or asymptomatic COVID-19 infectious people in the proposed model. The findings demonstrate the significance of vaccine doses on people with diabetes and individuals infectious with omicron variant. The proposed work helps with subsequent prevention efforts and the design of a vaccination policy to mitigate the effect of the novel coronavirus.

A nonlinear mathematical model on the Covid-19 transmission pattern among diabetic and non-diabetic population

In this paper, a three tier mathematical model describing the interactions between susceptible population, Covid-19 infected, diabetic population and Covid-19 infected, non diabetic population is proposed. Basic properties of such a dynamic model, namely, non negativity, boundedness of solutions, existence of disease-free and disease equilibria are studied and sufficient conditions are obtained. Basic reproduction number for the system is derived. Sufficient conditions on functionals and parameters of the system are obtained for the local as well as global stability of equilibria, thus, establishing the conditions for eventual prevalence of disease free or disease environment, as the case may be. The stability aspects are discussed in the context of basic reproduction number and vice versa. An important contribution of this article is that a novel technique is presented to estimate some key, influencing parameters of the system so that a pre-specified, assumed equilibrium state is approached eventually. This enables the society to prepare itself with the help of these key, influencing parameters so estimated. Several examples are provided to illustrate the results established and simulations are provided to visualize the examples.

Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination

In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.

Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis

Co-infection of Middle Eastern respiratory syndrome, coronavirus and tuberculosis, TB has a complex clinical entities that has estimated worldwide; mostly, in the Middle East. Clinical studies have shown that the propagation of disease is faster in (MERS-CoV) and TB co-infection compared to those of mono-infection. Clinical reports have shown that treatment of tuberculosis (TB) increase the risk of (MERS-CoV) reactivation. In this article, we propose an epidemic model to represents the Middle East respiratory syndrome coronavirus and tuberculosis (TB) co-infection. To do this, we first find the basic reproductive number and analyze the stability of the model. The stability conditions are obtained in term of the basic reproductive number. We also study the bifurcation analysis of the model, using the central manifold theory. Sensitivity of the basic reproductive number is performed to understand the most sensitive parameters. Finally, we show the feasibility of the analytical work, by numerical simulation.

Modelling the effect of vaccination on transmission dynamics of nervous necrosis virus in grouper larvae Epinephelus coioides

Nervous necrosis virus (NNV) infection in susceptible grouper larvae has been reported to cause high mortalities, leading to great economic losses in aquaculture industry. Although the effects of NNV vaccines on grouper have been broadly investigated, vaccination strategies have not been fully established. To this end, we introduced the parsimonious epidemiological models that explored the assessment of key epidemiological parameters and how they changed when vaccinations showed the effects. We showed that the models capture the published cumulative mortality data accurately. We estimated a basic reproduction number R₀  = 2.44 for NNV transmission in grouper larvae without vaccination. To effectively control NNV transmission by vaccination, a model for disease control was also generalized to attain the goals of controlled reproduction number less than 1. Our results indicated that at least 60% of grouper population needed to be immunized for ~75 min. Our data-driven modelling approach that links the transmission dynamics of NNV and vaccination strategies for grouper has the potential to support evidence-based planning and adaptation of integrated control measures. We encourage that the epidemiology-based framework introduced here can be further implemented for establishing effective vaccination and mitigation actions aimed at controlling diseases in fish farming practices.

Fractal dimension and synchronization of the controlled Julia sets of the SIRS model

It is of crucial significance to study the infectious disease phenomenon by using the SIRS model and thoughts of Julia set. In this paper, Julia set of the discrete version of the SIRS model is established to analyze the fractal dynamics of this model. Then, controller is designed to change the Julia set. Furthermore, the box-counting dimensions of the controlled Julia sets by selecting different appropriate parameters are computed to show the complexity of the model. Finally, a nonlinear coupling method is introduced to synchronize the Julia sets with different parameters of the same system. Simulation results show the efficacy of these methods.