Local and global stability of an HCV viral dynamics model with two routes of infection and adaptive immunity

The aim of this article is to formulate and study a mathematical model describing hepatitis C virus (HCV) infection dynamics. The model includes two essential modes of infection transmission, namely, virus-to-cell and cell-to-cell. The effect of therapy and adaptive immunity are incorporated in the suggested model. The adaptive immunity is represented by its two categories, namely, the humoral and cellular immune responses. Our article begins by establishing some mathematical results through proving the model's well-posedness in terms of existence, positivity and boundedness of solutions. We present all the steady states of the problem that depend on specific reproduction numbers. It moves then to the theoretical investigation of the local and global stability analysis of the free disease equilibrium and the four disease equilibria. The local and global stability analysis of the HCV mathematical model are established via the Routh-Hurwitz criteria and Lyapunov-LaSalle invariance principle, respectively. Finally, our article presents some numerical simulations to validate the analytical study of the global stability. Numerical simulations have shown the effect of the drug therapies on the system's dynamical behavior.

Analyzing evolutionary game theory in epidemic management: A study on social distancing and mask-wearing strategies

When combating a respiratory disease outbreak, the effectiveness of protective measures hinges on spontaneous shifts in human behavior driven by risk perception and careful cost-benefit analysis. In this study, a novel concept has been introduced, integrating social distancing and mask-wearing strategies into a unified framework that combines evolutionary game theory with an extended classical epidemic model. To yield deeper insights into human decision-making during COVID-19, we integrate both the prevalent dilemma faced at the epidemic's onset regarding mask-wearing and social distancing practices, along with a comprehensive cost-benefit analysis. We explore the often-overlooked aspect of effective mask adoption among undetected infectious individuals to evaluate the significance of source control. Both undetected and detected infectious individuals can significantly reduce the risk of infection for non-masked individuals by wearing effective facemasks. When the economical burden of mask usage becomes unsustainable in the community, promoting affordable and safe social distancing becomes vital in slowing the epidemic's progress, allowing crucial time for public health preparedness. In contrast, as the indirect expenses associated with safe social distancing escalate, affordable and effective facemask usage could be a feasible option. In our analysis, it was observed that during periods of heightened infection risk, there is a noticeable surge in public interest and dedication to complying with social distancing measures. However, its impact diminishes beyond a certain disease transmission threshold, as this strategy cannot completely eliminate the disease burden in the community. Maximum public compliance with social distancing and mask-wearing strategies can be achieved when they are affordable for the community. While implementing both strategies together could ultimately reduce the epidemic's effective reproduction number ([Formula: see text]) to below one, countries still have the flexibility to prioritize either of them, easing strictness on the other based on their socio-economic conditions.

Chaos and bifurcations of a two-dimensional hepatitis C virus model with hepatocyte homeostasis

In this paper, we delve into the intricate local dynamics at equilibria within a two-dimensional model of hepatitis C virus (HCV) alongside hepatocyte homeostasis. The study investigates the existence of bifurcation sets and conducts a comprehensive bifurcation analysis to elucidate the system's behavior under varying conditions. A significant focus lies on understanding how changes in parameters can lead to bifurcations, which are pivotal points where the qualitative behavior of the system undergoes fundamental transformations. Moreover, the paper introduces and employs hybrid control feedback and Ott-Grebogi-Yorke strategies as tools to manage and mitigate chaos inherent within the HCV model. This chaos arises due to the presence of flip and Neimark-Sacker bifurcations, which can induce erratic behavior in the system. Through the implementation of these control strategies, the study aims to stabilize the system and restore it to a more manageable and predictable state. Furthermore, to validate the theoretical findings and the efficacy of the proposed control strategies, extensive numerical simulations are conducted. These simulations serve as a means of confirming the theoretical predictions and provide insight into the practical implications of the proposed control methodologies. By combining theoretical analysis with computational simulations, the paper offers a comprehensive understanding of the dynamics of the HCV model and provides valuable insights into potential strategies for controlling and managing chaos in such complex biological systems.

Hepatitis C virus fractional-order model: mathematical analysis

Mathematical analysis of epidemics is crucial for the prediction of diseases over time and helps to guide decision makers in terms of public health policy. It is in this context that the purpose of this paper is to study a fractional-order differential mathematical model of HCV infection dynamics, incorporating two fundamental modes of transmission of the infection; virus-to-cell and cell-to-cell along with a cure rate of infected cells. The model includes four compartments, namely, the susceptible hepatocytes, the infected ones, the viral load and the humoral immune response, which is activated in the host to attack the virus. Each compartment involves a long memory effect that is modeled by a Caputo fractional derivative. Our paper starts with the investigation of some basic analytical results. First, we introduce some preliminaries about the needed fractional calculus tools. Next, we establish the well-posedness of our mathematical model in terms of proving the existence, positivity and boundedness of solutions. We present the different problem steady states depending on some reproduction numbers. After that, the paper moves to the stage of proving the global stability of the three steady states. To evaluate the theoretical study of the global stability, we apply a numerical method based on the fundamental theorem of fractional calculus as well as a three-step Lagrange polynomial interpolation method. The numerical simulations show that the free-endemic equilibrium is stable if the basic reproduction number is less than unity. In addition, the numerical tests demonstrate the stability of the other endemic equilibria under some optimal conditions. It is observed that the numerical simulations and the founding theoretical results are coherents.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

Projections and fractional dynamics of COVID-19 with optimal control strategies

When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, unprecedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention strategies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Bangladesh and India. Control reproduction numbers ( R c ) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. Nevertheless, as the pandemic is not over in any country, it is highly recommended to use efficacious face coverings and maintain strict physical distancing in public gatherings. All necessary graphical simulations have been performed with the help of Caputo-Fabrizio fractional derivatives. In addition, optimal control strategies for fractional system have been designed and the existence of unique solution has also been showed using Picard-Lindelof technique. Finally, unconditional stability of the fractional numerical technique has been proved.

Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives

In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number, R 0 of the model has been presented. Cameroon has been considered as a representative for the developing countries and the epidemic threshold, R 0 has been estimated to be  ~ 3.41 ( 95 % CI : 2.2 - 4.4 ) as of July 9, 2020. Using real data compiled by the Cameroonian government, model calibration has been performed through an optimization algorithm based on renowned trust-region-reflective (TRR) algorithm. Based on our projection results, the probable peak date is estimated to be on August 1, 2020 with approximately 1073 ( 95 % CI : 714 - 1654 ) daily confirmed cases. The tally of cumulative infected cases could reach  ~ 20, 100 ( 95 % CI : 17 , 343 - 24 , 584 ) cases by the end of August 2020. Later, global sensitivity analysis has been applied to quantify the most dominating model mechanisms that significantly affect the progression dynamics of COVID-19. Importantly, Caputo derivative concept has been performed to formulate a fractional model to gain a deeper insight into the probable peak dates and sizes in Cameroon. By showing the existence and uniqueness of solutions, a numerical scheme has been constructed using the Adams-Bashforth-Moulton method. Numerical simulations have enlightened the fact that if the fractional order α is close to unity, then the solutions will converge to the integer model solutions, and the decrease of the fractional-order parameter (0  <  α  <  1) leads to the delaying of the epidemic peaks.

Forecasting COVID-19 pandemic: A data-driven analysis

In this paper, a new Susceptible-Exposed-Symptomatic Infectious-Asymptomatic Infectious-Quarantined-Hospitalized-Recovered-Dead (SEI_DI_UQHRD) deterministic compartmental model has been proposed and calibrated for interpreting the transmission dynamics of the novel coronavirus disease (COVID-19). The purpose of this study is to give tentative predictions of the epidemic peak for Russia, Brazil, India and Bangladesh which could become the next COVID-19 hotspots in no time by using a newly developed algorithm based on well-known Trust-region-reflective (TRR) algorithm, which is one of the robust real-time optimization techniques. Based on the publicly available epidemiological data from late January until 10 May, it has been estimated that the number of daily new symptomatic infectious cases for the above mentioned countries could reach the peak around the middle of June with the peak size of  ∼ 15, 774 (95% CI, 12,814-16,734) symptomatic infectious cases in Russia,  ∼ 26, 449 (95% CI, 25,489-31,409) cases in Brazil,  ∼ 9, 504 (95% CI, 8,378-13,630) cases in India and  ∼ 2, 209 (95% CI, 2,078-2,840) cases in Bangladesh if current epidemic trends hold. As of May 11, 2020, incorporating the infectiousness capability of asymptomatic carriers, our analysis estimates the value of the basic reproductive number (R ₀) was found to be  ∼ 4.234 (95% CI, 3.764-4.7) in Russia,  ∼ 5.347 (95% CI, 4.737-5.95) in Brazil,  ∼ 5.218 (95% CI, 4.56-5.81) in India,  ∼ 4.649 (95% CI, 4.17-5.12) in the United Kingdom and  ∼ 3.53 (95% CI, 3.12-3.94) in Bangladesh. Moreover, Latin hypercube sampling-partial rank correlation coefficient (LHS-PRCC) which is a global sensitivity analysis (GSA) method has been applied to quantify the uncertainty of our model mechanisms, which elucidates that for Russia, the recovery rate of undetected asymptomatic carriers, the rate of getting home-quarantined or self-quarantined and the transition rate from quarantined class to susceptible class are the most influential parameters, whereas the rate of getting home-quarantined or self-quarantined and the inverse of the COVID-19 incubation period are highly sensitive parameters in Brazil, India, Bangladesh and the United Kingdom which could significantly affect the transmission dynamics of the novel coronavirus disease (COVID-19). Our analysis also suggests that relaxing social distancing restrictions too quickly could exacerbate the epidemic outbreak in the above-mentioned countries.