Global dynamics of a piece-wise epidemic model with switching vaccination strategy

A piece-wise epidemic model of a switching vaccination program, implemented once the number of people exposed to a disease-causing virus reaches a critical level, is proposed. In addition, variation or uncertainties in interventions are examined with a perturbed system version of the model. We also analyzed the global dynamic behaviors of both the original piece-wise system and the perturbed version theoretically, using generalized Jacobian theory, Lyapunov constants for a non-smooth vector field and a generalization of Dulac's criterion. The main results show that, as the critical value varies, there are three possibilities for stabilization of the piece-wise system: (i) at the disease-free equilibrium; (ii) at the endemic states for the two subsystems or (iii) at a generalized equilibrium which is a novel global attractor for non-smooth systems. The perturbed system exhibits new global attractors including a pseudo-focus of parabolic-parabolic (PP) type, a pseudo-equilibrium and a crossing cycle surrounding a sliding mode region. Our findings demonstrate that an infectious disease can be eradicated either by increasing the vaccination rate or by stabilizing the number of infected individuals at a previously given level, conditional upon a suitable critical level and the parameter values

Piecewise virus-immune dynamic model with HIV-1 RNA-guided therapy

Clinical studies have used CD4 T cell counts to evaluate the safety or risk of plasma HIV-1 RNA-guided structured treatment interruptions (STIs), aimed at maintaining CD4 T cell counts above a safe level and plasma HIV-1 RNA below a certain level. However, quantifying and evaluating the impact of STIs on the control of HIV replication and on activation of the immune response remains challenging. Here we extend the virus-immune dynamic system by including a piecewise smooth function to describe the elimination of HIV viral loads and the activation of effector cells under plasma HIV-1 RNA-guided therapy, in order to quantitatively explore the STI strategies. We theoretically investigate the global dynamics of the proposed Filippov system. Our main results indicate that HIV viral loads could either go to infinity or be maintained below a certain level or stabilize at a previously given level, depending on the threshold level and initial HIV virus loads and effector cell counts. This suggests that proper combinations of threshold and initial HIV virus loads and effector cell counts, based on threshold policy, can successfully preclude exceptionally high growth of HIV virus and, in particular, maximize the controllable region

Coupled Evolutionary Behavioral and Disease Dynamics under Reinfection Risk

We study the interplay between epidemic dynamics and human decision making for epidemics that involve reinfection risk; in particular, the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered-infected (SIRI) epidemic models. In the proposed game-theoretic setting, individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. For the SIS epidemic, we fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system for both SIS and SIRI models. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.Comment: arXiv admin note: text overlap with arXiv:2203.1027

Media impact research: a discrete SIR epidemic model with threshold switching and nonlinear infection forces

The media's coverage has the potential to impact human behavior and aid in the control of emergent infectious diseases. We aim to quantify and evaluate the extent to which media coverage can influence infectious disease control through a mathematical model, thus proposing a switching epidemic model that considers the effect of media coverage. The threshold strategy incorporates media influence only when the number of infected cases surpasses a specific threshold; otherwise, it is disregarded. When conducting qualitative analysis of two subsystems, focusing on the existence and stability of equilibria. Using numerical methods, the codimension-2 bifurcation analysis is adopted here to investigate the various types of equilibria within the switching system that play a vital role in pest control. On the other hand, codimension-1 bifurcation analysis reveals the existence of periodic, chaotic solutions, period-doubling bifurcations, multiple attractors and other complexities within the proposed model, which could pose challenges in disease control. Additionally, the impact of key parameters on epidemic outbreaks is analyzed, such as the initial values of susceptible and infective individuals, and discuss the potential benefits of mass media coverage in preventing emerging infectious diseases. The modeling and analytical techniques developed for threshold control strategies can be applied to other disease control efforts

Modelling and controlling infectious diseases

The financial support by IDRC has made it much easier to put together network activities involving scientists in both countries, a special example is the large presence of the Chinese students in the 2012 Summer School on Mathematics for Public Health the Canadian group organized in Edmonton in May of 2012.Infectious disease control is a major challenge in China due to China’s fast growing economy, changing social networks and evolving health service infrastructures. The success of disease control in China has a profound impact beyond its borders. In support of better disease control, this five year research program was designed to enhance China’s national capacity for analyzing, modeling and predicting transmission dynamics of infectious diseases through joint research, training young scientists, and building collaborative relationships. This successful program was led by the National Center for AIDS/STD Control and Prevention (Chinese Centre for Disease Control and Prevention, China) and the Centre for Disease Modeling (York University, Canada), and involved a number of Canadian and Chinese universities in various areas of infectious disease modelling and control. The bilateral collaboration also trained numerous highly qualified personnel and built a network for sustaining collaboration. This capacity building was facilitated by joint projects and bilateral annual meetings in major cities in China and Canada. The research activities on modeling major public health threats of infectious diseases focused on major diseases in China and/or issues of global public health concern including HIV transmission and prevention among high risk population, HIV treatment and drug resistance, influenza, schistosomiasis, mutation and stemma of SIV and HIV, latent and active tuberculosis infection, HBV control and vaccination. The outputs of the project were reported through peer-reviewed publications and modelling– based and science-informed public policy recommendations

Study of Mathematical Modeling for Plant Disease Transmission: A Systematic Literature Review during 2012-2022

Many models representing disease transmission have been constructed and analyzed mathematically. However, literature studies on the mathematical models for vector-borne disease are sparse, especially on the plant disease transmission model. This study aims to obtain information about the research conducted and find room for developing the model, including mathematical analysis, intervention used, and biological factors considered. We employ a Systematic Literature Review (SLR) to explore all of the studies on plant disease transmission modeling collected from four digital databases. First, the JabRef reference manager helps conduct the inclusion and exclusion processing. Then, we obtain 60 selected articles that passed the criterion. Next, the VOSviewer application is resulting a bibliometric analysis of the database containing chosen articles. Finally, we classify the model constructed based on the system used and elaborate on the intervention used. The results show that the existing researcher clusters are not linked to each other, and the models only consider usual interventions such as roguing and insecticide spraying. Hence, there is much room to build collaboration between the researcher and develop models for plant disease transmission by considering the other various intervention and biological factors in the model to improve further

Modelling of Human Behaviour and Response to the Spread of Infectious Diseases

We incorporate two types of human behavioural changes into the epidemic models. First, a two-subpopulation imitation dynamic model is constructed via the replicator dynamical equations to study the self-initiated pre-cautionary health protective behaviour under the cost-benefit considerations and group pressure. Second, the impacts of additional characteristics of imperfect vaccine and the asymmetric property of smoothed best response on the vaccination behaviour are studied within the vaccination population game framework, and via the Gompertz function, respectively

Numerical treatment for mathematical model of farming awareness in crop pest management

The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios