Final epidemic size and optimal control of socio-economic multi-group influenza model.

Flu, a common respiratory disease is caused mainly by the influenza virus. The Avian influenza (H5N1) outbreaks, as well as the 2009 H1N1 pandemic, have heightened global concerns about the emergence of a lethal influenza virus capable of causing a catastrophic pandemic. During the early stages of an epidemic a favourable change in the behaviour of people can be of utmost importance. An economic status-based (higher and lower economic class) structured model is formulated to examine the behavioural effect in controlling influenza. Following that, we have introduced controls into the model to analyse the efficacy of antiviral treatment in restraining infections in both economic classes and examined an optimal control problem. We have obtained the reproduction number R 0 along with the final epidemic size for both the strata and the relation between reproduction number and epidemic size. Through numerical simulation and global sensitivity analysis, we have shown the importance of the parameters ϕ i , ϕ s , η 2 , ß and θ on reproduction number. Our result shows that by increasing ϕ 1 , η 2 and by decreasing ß , θ and ϕ s , we can reduce the infection in both the economic group. As a result of our analysis, we have found that the reduction of infections and their level of adversity is directly influenced by positive behavioural patterns or changes as without control susceptible population is increased by 23 % , the infective population is decreased by 48.54 % and the recovered population is increased by 23.23 % in the higher economic group who opted changed behaviour as compared to the lower the economic group (people living with normal behaviour). Thus normal behaviour contributes to the spread and growth of viruses and adds to the hassle. We also examined how antiviral drug control impacts both economic strata and found that in the higher economic strata, the susceptible population increased by 53.84 % , the infective population decreased by 33.6 % and the recovered population improved by 62.29 % as compared to the lower economic group, the susceptible population has increased by 19.04 % , the infective population is decreased by 17.29 % and the recovered population is improved by 47.82 % . Our results enlighten the role that how different behaviour in separate socio-economic class plays an important role in changing the dynamics of the system and also affects the basic reproduction number. The results of our study suggest that it is important to adopt a modified behaviour like social distancing, wearing masks accompanying the time-dependent controls in the form of an antiviral drug's effectiveness to combat infections and increasing the proportion of the susceptible population.

Analysing an epidemic-economic model in the presence of novel corona virus infection: capital stabilization, media effect, and the role of vaccine.

The pandemic being a health issue at its core is a multifaceted crisis encompassing both economic and epidemic factors in a twisted tale of challenges. In counteraction, we have proposed a combined epidemic-economic model that analyses system dynamics arising in the presence of an infectious disease (SARS-2-COVID-19 in our case). Dynamical analysis of the system has been performed in context to the equilibria along with local and global stability analysis of the system simultaneously visualizing the effect on capital stabilization. The global stability analysis has been performed using graph-theoretic method. Curve-Fit has been performed for the system using optimization algorithm. The relation between all the parameters and variables involved in the model has been explored by calculating sensitivity indices which gives us the proportion that a relative change in a parameter brings to the relative change in a variable. Our findings reveal that (1) Vaccination instigates economic growth (with evidence of data obtained for 24 countries). (2) Complete vaccination leads to a considerable reduction in all infections (reduction up to 90%, as per current CDC study). (3) Excessive exposure to media can facilitate spike in infections. (4) Parameter sensitivity analysis can be of immense help in policy formation.

Burden of cytokines storm on prognosis of SARS-CoV-2 infection through immune response: dynamic analysis and optimal control with immunomodulatory therapy.

Immune responses have a crucial role to play against SARS-CoV-2 virus as the adaptive and innate immune systems of the human body help restoring the body to a healthy stage by annihilating this deadly viral infection. Cytokines also play a significant role in modulating a balance between innate and adaptive immune responses but excess of it can have a detrimental affect on critically ill patients. Therefore, this paper is a novel attempt to formulate a within-host mathematical model showing the impact of cytokines storm on healthy cells. The dynamics of the system is analysed which involves basic reproduction number, steady state solutions and global dynamics for disease-free point and endemic equilibrium using geometric approach. Further, an optimal control problem is discussed considering immunomodulatory therapy (targeting cytokines signaling) as control using linear feedback control method to increase the level of healthy cells, which provides vitality for our system. Through numerical simulations, analytic solutions are validated followed by the curve-fit for the cytokines using real data and an optimization algorithm for optimal fit. Finally, sensitivity analysis for the basic reproduction number and the rate of change of healthy cells using Latin Hypercube Sampling method (LHS) is performed. Our finding suggests that immunomodulatory therapy (tocilizumab) can act as a key component to control cytokines storm for critically ill patients to restore the body to a healthy state.

The Hard Lessons and Shifting Modeling Trends of COVID-19 Dynamics: Multiresolution Modeling Approach.

The COVID-19 pandemic has placed epidemiologists, modelers, and policy makers at the forefront of the global discussion of how to control the spread of coronavirus. The main challenges confronting modelling approaches include real-time projections of changes in the numbers of cases, hospitalizations, and fatalities, the consequences of public health policy, the understanding of how best to implement varied non-pharmaceutical interventions and potential vaccination strategies, now that vaccines are available for distribution. Here, we: (i) review carefully selected literature on COVID-19 modeling to identify challenges associated with developing appropriate models along with collecting the fine-tuned data, (ii) use the identified challenges to suggest prospective modeling frameworks through which adaptive interventions such as vaccine strategies and the uses of diagnostic tests can be evaluated, and (iii) provide a novel Multiresolution Modeling Framework which constructs a multi-objective optimization problem by considering relevant stakeholders' participatory perspective to carry out epidemic nowcasting and future prediction. Consolidating our understanding of model approaches to COVID-19 will assist policy makers in designing interventions that are not only maximally effective but also economically beneficial.