Modeling the dynamics of viral infections in presence of latently infected cells

Modelling and analysis of the HIV/AIDS epidemic with fast and slow asymptomatic infections in China from 2008 to 2021

The aim of this paper is to investigate the spread of the HIV/AIDS epidemic in China during 2008-2021. A new mathematical model is proposed to study the dynamics of HIV transmission with acute infection, fast asymptomatic infections, and slow asymptomatic infections. The basic reproduction number is obtained by the next-generation matrix method. A quantitative analysis of the model, including the local behavior, global behavior, and permanence, is performed. Numerical simulations are presented to enhance the results of these analyses. The behavior or the model's parameters are estimated from real data. A sensitivity analysis shows that the proportion of asymptomatic infections co-infected with other diseases significantly affects the basic reproduction number. We further analyze the impact of implementing single and multiple measure(s) in parallel with the epidemic. The study results conclude that multiple measures are more effective in controlling the spread of AIDS compared to just one. The HIV epidemic can be effectively curbed by reducing the contact rate between fast asymptomatic infected individuals and susceptible populations, increasing the early diagnosis and screening of HIV-infected individuals co-infected with other diseases, and treating co-infected patients promptly.

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.

Behavioral response of population on transmissibility and saturation incidence of deadly pandemic through fractional order dynamical system

The world entered in another wave of the SARS-CoV-2 due to non-compliance of standard operating procedures appropriately, initiated by respective governments. Apparently, measures like using face masks and social distancing were not observed by populace that ultimately worsens the situation. The behavioral response of the population induces a change in the dynamical outcomes of the pandemic, which is documented in this paper for all intents and purposes. The innovative perception is executed through a compartmental model with the incorporation of fractional calculus and saturation incident rate. In the first instance, the epidemiological model is designed with proportional fractional definition considering the compartmental individuals of susceptible, social distancing, exposed, quarantined, infected, isolated and recovered populations. By virtue of proportional fractional derivative, effective dynamical outcomes of equilibrium states and basic reproduction number are successfully elaborated with memory effect. The expansion of this derivative greatly simplifies the model to integer order while remaining in the fractional context. Subsequently, the memory effects on the asymptotic profiles are demonstrated through various graphical plots and tabulated values. In addition, the inclusion of saturation incident rate further explains the transmissibility of infection for different behavior of susceptible individuals. Mathematically, the results are also validated through comparative analysis of values with the solutions attained from fractional fourth order Runge-Kutta method (FRK4).

Dynamic analysis of the mathematical model of COVID-19 with demographic effects

The coronavirus is currently extremely contagious for humankind, which is a zoonotic tropical disease. The pandemic is the largest in history, affecting almost the whole world. What makes the condition the worst of all is no specific effective treatment available. In this article, we present an extended and modified form of SIR and SEIR model, respectively. We begin by investigating a simple mathematical model that describes the pandemic. Then we apply different safety measures to control the pandemic situation. The mathematical model with and without control is solved by using homotopy perturbation method. Obtained solutions have been presented graphically. Finally, we develop another mathematical model, including quarantine and hospitalization.

How relevant is the decision of containment measures against COVID-19 applied ahead of time?

The cumulative number of confirmed infected individuals by the new coronavirus outbreak until April 30th, 2020, is presented for the countries: Belgium, Brazil, United Kingdom (UK), and the United States of America (USA). After an initial period with a low incidence of newly infected people, a power-law growth of the number of confirmed cases is observed. For each country, a distinct growth exponent is obtained. For Belgium, UK, and USA, countries with a large number of infected people, after the power-law growth, a distinct behavior is obtained when approaching saturation. Brazil is still in the power-law regime. Such updates of the data and projections corroborate recent results regarding the power-law growth of the virus and their strong Distance Correlation between some countries around the world. Furthermore, we show that act in time is one of the most relevant non-pharmacological weapons that the health organizations have in the battle against the COVID-19, infectious disease caused by the most recently discovered coronavirus. We study how changing the social distance and the number of daily tests to identify infected asymptomatic individuals can interfere in the number of confirmed cases of COVID-19 when applied in three distinct days, namely April 16th (early), April 30th (current), and May 14th (late). Results show that containment actions are necessary to flatten the curves and should be applied as soon as possible.

Dynamics of an HIV model with cytotoxic T-lymphocyte memory

We consider a four-dimensional HIV model that includes healthy cells, infected cells, primary cytotoxic T-lymphocyte response (CTLp), and secondary cytotoxic T-lymphocyte response (CTLe). The CTL memory generation depends on CD4⁺ T-cell help, and infection of CD4⁺ T cells results in impaired T-cell help. We show that the system has up to five equilibria. By the Routh-Hurwitz theorem and central manifold theorem we obtain some sufficient conditions for the local stability, globally stability of the equilibria, and the bifurcations. We still discover the bistability case where in the system there may coexist two stable equilibria or a stable equilibrium together with a stable limit cycle. Several numerical analyses are carried out to illustrate the validity of our theoretical results.

Modeling and forecasting the spread tendency of the COVID-19 in China

To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on collected data that were issued by the National Health Commission of China (NHCC) from January 10 to March 3. The model was used to forecast the spread tendency of the disease. The key factors influencing the epidemic were explored through modulation of the parameters, including the removal rate, the average number of the infected contacting the susceptible per day and the average number of the exposed contacting the susceptible per day. The correlation of the infected is 99.9% between established model data in this study and issued data by NHCC from January 10 to February 15. The correlation of the removed, the death and the cured are 99.8%, 99.8% and 99.6%, respectively. The average forecasting error rates of the infected, the removed, the death and the cured are 0.78%, 0.75%, 0.35% and 0.83%, respectively, from February 16 to March 3. The peak time of the epidemic forecast by our established model coincided with the issued data by NHCC. Therefore, our study established a mathematical model with high accuracy. The aforementioned parameters significantly affected the trend of the epidemic, suggesting that the exposed and the infected population should be strictly isolated. If the removal rate increases to 0.12, the epidemic will come to an end on May 25. In conclusion, the proposed mathematical model accurately forecast the spread tendency of COVID-19 in China and the model can be applied for other countries with appropriate modifications.