The stability analysis of a co-circulation model for COVID-19, dengue, and zika with nonlinear incidence rates and vaccination strategies.

This paper aims to study the impacts of COVID-19 and dengue vaccinations on the dynamics of zika transmission by developing a vaccination model with the incorporation of saturated incidence rates. Analyses are performed to assess the qualitative behavior of the model. Carrying out bifurcation analysis of the model, it was concluded that co-infection, super-infection and also re-infection with same or different disease could trigger backward bifurcation. Employing well-formulated Lyapunov functions, the model's equilibria are shown to be globally stable for a certain scenario. Moreover, global sensitivity analyses are performed out to assess the impact of dominant parameters that drive each disease's dynamics and its co-infection. Model fitting is performed on the actual data for the state of Amazonas in Brazil. The fittings reveal that our model behaves very well with the data. The significance of saturated incidence rates on the dynamics of three diseases is also highlighted. Based on the numerical investigation of the model, it was observed that increased vaccination efforts against COVID-19 and dengue could positively impact zika dynamics and the co-spread of triple infections.

Effective Analysis and Investigation in COVID-19 Prevention Policies Based on Population Dynamics Modeling and Simulation

The paper proposes a population dynamics model to simulate the COVID-19 pandemic and analyze the effectiveness of prevention policies in the early stage. The model is designed to aid the decision-making process of policy-making in the early stage. The model is formulated based on the SEIR model to simulate the spread of COVID19 from human to human. By implementing the data in the U.S., the model is first fitted to the data first. Then, the model simulates the number of infected people with the change of time under different levels of social distancing and mask-wearing. © 2022 IEEE.

Application of optimal control to the dynamics of COVID-19 disease in South Africa.

SARS-CoV-2 (COVID-19) belongs to the beta-coronavirus family, which include: the severe acute respiratory syndrome coronavirus (SARS-CoV) and the Middle East respiratory syndrome coronavirus (MERS-CoV). Since its outbreak in South Africa in March 2020, it has lead to high mortality and thousands of people contracting the virus. Mathematical analysis of a model without controls was done and the basic reproduction number ( R 0 ) of the COVID-19 for the South African pandemic determined. Permissible controls were introduced and an optimal control problem using the Pontraygain Maximum Principle is formulated. Numerical findings suggest that joint implementation of effective mask usage, physical distancing and active screening and testing, are effective measures to curtail the spread of the disease in the human population. The results obtained in this paper are of public health importance in the control and management of the spread for the novel coronavirus, SARS-CoV-2, in South Africa.

epidWaves: A code for fitting multi-wave epidemic models.

The COVID-19 pandemic has given rise to a great demand for computational models capable of describing and inferring the evolution of an epidemic outbreak in the short term. In this sense, we introduce epidWaves, a package that provides a framework for fitting multi-wave epidemic models to data from actual outbreaks of COVID-19 and other infectious diseases.

Development of a Robust Mathematical Model to Estimate COVID-19 Cases in Lebanon Based on SEIRDV Modified Model

COVID-19 pandemic triggered a global crisis, whether it comes to a huge global health emergency or to the global economic crisis situation. It is one of the greatest challenges this generation is facing. Computational simulations are playing a huge rule in the prediction of the current pandemic. Such simulations enable early predictions for future projections of the pandemic and are useful to estimate the efficiency of control action taken against this virus. The SEIR (Susceptible-Exposed-Infectious-Recovered) model is a commonly used model to compute the simulations of any infectious viral diseases and was widely used before to model and simulate SARS, EBOLA, Spanish Flu, etc. This paper presents a modified SEIR model with additional parameters taken into consideration such as the death, recovered and recovered with the chance of being infected again, vaccination and control efficiency;where the control represents the effectiveness of the lockdown. This factor is being controlled in order to extend the projections into controlled death, recovery, and infection. Specific information including time delay on the development of the pandemic due to control action measures, ageing factor of the population, and resusceptibility with temporal immune response are also included in the model. After that, the model examines the outcome of the system after adding a controllable vaccine with taking into consideration the vaccination rate and vaccine's efficacy. The numerical results are demonstrated to show the predictability range of this model.

Mathematical Modeling of the Novel Coronavirus Pandemic in Iran: A Model With Vaccination

The novel coronavirus (COVID-19) is a major health threat caused by a virus called Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). COVID-19 can cause acute respiratory illness, which is deadly in some people. Epidemio-logically, vaccination is the safest and most effective approach to gaining immunity and fighting against viral diseases. In this paper, the extended compartmental SEIR model, considering vaccination as a pharmaceutical intervention, to assess the behavior of the COVID-19 outbreak in Iran is proposed. Initially, some mathematical analysis of the model, including positivity, boundedness, the basic reproduction number, and herd immunity is investigated. In order to validate the proposed model, the biological parameters of the model are estimated based on real-confirmed cases in Iran at a specified interval of time. Finally, to examine the concept of flattening the curve of the disease outbreak, the impacts of physical distancing and vaccination on mitigating the burden of the epidemic are compared graphically. © 2022 IEEE.

The art of fitting ordinary differential equations models to experimental results

Advanced fitting of ordinary differential equations models to experimental results is presented within the context of different academic levels of students and diverse research fields. In many areas, the analysis of experimental results cannot be restricted to cases where particular solutions of the models' differential equations, valid only for specific limit conditions, apply. In those cases, analytical mathematical equations are not available and a complete description of the systems extends beyond the numerical minimization of statistical estimators, like the chi-square, because it requires solving numerically the models' differential equations. Dedicated fitting procedures that involve the interdependent processes of solving the ordinary differential equations and fitting the numerical solutions to the experimental results are required to obtain the best fitting sets of parameters with consistent physical meaning. A simple, but powerful, web-based ordinary differential equations solver and fitter is presented, and used to analyse both the complete motion of a rigid pendulum and the dynamics of a viral infection.

Advanced Muti-Mutation with Intervention Policies Pandemic Model

A pandemic is a threat to humanity with potentially millions of deaths worldwide. Epidemiological models can be used to better understand pandemic dynamics and assist policymakers in optimizing their Intervention Policies (IPs). Most existing epidemiological models assume, sometimes incorrectly, that a pandemic is caused by a single pathogen, ignoring pathogen mutations over time that result in different pathogen variants with different characteristics. In addition, the existing models do not incorporate the effect of IPs like vaccinations and lockdowns during the fitting phase. In this work, we introduce a new multi-mutation model called Suspected-Infected-Vaccinated-Recovered-reInfected (SIVRI). This model extends the SIRS model with adaptation to incorporate available knowledge related to the different pathogen mutations together with multiple IPs. In order to find the model parameters we propose a new fitting procedure that supports the complex social, epidemiological, and clinical dynamics that occur during a pandemic. We examine the suggested SIVRI model in comparison to the SIRS and XGboost models on the COVID-19 pandemic in Israel that includes four COVID-19 mutations, and the vaccination and lockdown IPs. We show that the proposed model can fit accurately to the historical data and outperform the existing models in predictions of basic reproduction number, mortality rate, and severely infected individuals rate. Author

A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana-Baleanu derivative.

This paper considers and analyzes a fractional order model for COVID-19 and tuberculosis co-infection, using the Atangana-Baleanu derivative. The existence and uniqueness of the model solutions are established by applying the fixed point theorem. It is shown that the model is locally asymptotically stable when the reproduction number is less than one. The global stability analysis of the disease free equilibrium points is also carried out. The model was simulated using data relevant to both diseases in New Delhi, India. Fitting the model to the cumulative confirmed COVID-19 cases for New Delhi from March 1, 2021 to June 26, 2021, COVID-19 and TB contact rates and some other important parameters of the model are estimated. The numerical method used combines the two-step Lagrange polynomial and the fundamental theorem of fractional calculus and has been shown to be highly accurate and efficient, user-friendly and converges quickly to the exact solution even with a large step of discretization. Simulations of the Fractional order model revealed that reducing the risk of COVID-19 infection by latently-infected TB individuals will not only bring down the burden of COVID-19, but will also reduce the co-infection of both diseases in the population. Also, the conditions for the co-existence or elimination of both diseases from the population are established.

Mathematical model of COVID-19 in Nigeria with optimal control.

The novel Coronavirus Disease 2019 (COVID-19) is a highly infectious disease caused by a new strain of severe acute respiratory syndrome of coronavirus 2 (SARS-CoV-2). In this work, we proposed a mathematical model of COVID-19. We carried out the qualitative analysis along with an epidemic indicator which is the basic reproduction number ( R 0 ) of this model, stability analysis of COVID-19 free equilibrium (CFE) and Endemic equilibrium (EE) using Lyaponuv function are considered. We extended the basic model into optimal control system by incorporating three control strategies. These are; use of face-mask and hand sanitizer along with social distancing; treatment of COVID-19 patients and active screening with testing and the third control is prevention against recurrence and reinfection of humans who have recovered from COVID-19. Daily data given by Nigeria Center for Disease Control (NCDC) in Nigeria is used for simulation of the proposed COVID-19 model to see the effects of the control measures. The biological interpretation of this findings is that, COVID-19 can be effectively managed or eliminated in Nigeria if the control measures implemented are capable of taking or sustaining the basic reproductive number R 0 to a value below unity. If the three control strategies are well managed by the government namely; NCDC, Presidential Task Force (PTF) and Federal Ministry of Health (FMOH) or policymakers, then COVID-19 in Nigeria will be eradicated.

Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria.

This work examines the impact of various non-pharmaceutical control measures (government and personal) on the population dynamics of the novel coronavirus disease 2019 (COVID-19) in Lagos, Nigeria, using an appropriately formulated mathematical model. Using the available data, since its first reported case on 16 March 2020, we seek to develop a predicative tool for the cumulative number of reported cases and the number of active cases in Lagos; we also estimate the basic reproduction number of the disease outbreak in the aforementioned State in Nigeria. Using numerical simulations, we show the effect of control measures, specifically the common social distancing, use of face mask and case detection (via contact tracing and subsequent testings) on the dynamics of COVID-19. We also provide forecasts for the cumulative number of reported cases and active cases for different levels of the control measures being implemented. Numerical simulations of the model show that if at least 55% of the population comply with the social distancing regulation with about 55% of the population effectively making use of face masks while in public, the disease will eventually die out in the population and that, if we can step up the case detection rate for symptomatic individuals to about 0.8 per day, with about 55% of the population complying with the social distancing regulations, it will lead to a great decrease in the incidence (and prevalence) of COVID-19.