Mutations make pandemics worse or better: modeling SARS-CoV-2 variants and imperfect vaccination

COVID-19 is a respiratory disease triggered by an RNA virus inclined to mutations. Since December 2020, variants of COVID-19 (especially Delta and Omicron) continuously appeared with different characteristics that influenced death and transmissibility emerged around the world. To address the novel dynamics of the disease, we propose and analyze a dynamical model of two strains, namely native and mutant, transmission dynamics with mutation and imperfect vaccination. It is also assumed that the recuperated individuals from the native strain can be infected with mutant strain through the direct contact with individual or contaminated surfaces or aerosols. We compute the basic reproduction number, R 0 , which is the maximum of the basic reproduction numbers of native and mutant strains. We prove the nonexistence of backward bifurcation using the center manifold theory, and global stability of disease-free equilibrium whenR 0 < 1 , that is, vaccine is effective enough to eliminate the native and mutant strains even if it cannot provide full protection. Hopf bifurcation appears when the endemic equilibrium loses its stability. An intermediate mutation rate ν 1 leads to oscillations. When ν 1 increases over a threshold, the system regains its stability and exhibits an interesting dynamics called endemic bubble. An analytical expression for vaccine-induced herd immunity is derived. The epidemiological implication of the herd immunity threshold is that the disease may effectively be eradicated if the minimum herd immunity threshold is attained in the community. Furthermore, the model is parameterized using the Indian data of the cumulative number of confirmed cases and deaths of COVID-19 from March 1 to September 27 in 2021, using MCMC method. The cumulative cases and deaths can be reduced by increasing the vaccine efficacies to both native and mutant strains. We observe that by considering the vaccine efficacy against native strain as 90%, both cumulative cases and deaths would be reduced by 0.40%. It is concluded that increasing immunity against mutant strain is more influential than the vaccine efficacy against it in controlling the total cases. Our study demonstrates that the COVID-19 pandemic may be worse due to the occurrence of oscillations for certain mutation rates (i.e., outbreaks will occur repeatedly) but better due to stability at a lower infection level with a larger mutation rate. We perform sensitivity analysis using the Latin Hypercube Sampling methodology and partial rank correlation coefficients to illustrate the impact of parameters on the basic reproduction number, the number of cumulative cases and deaths, which ultimately sheds light on disease mitigation.

Assessing potential insights of an imperfect testing strategy: Parameter estimation and practical identifiability using early COVID-19 data in India

A deterministic model with testing of infected individuals has been proposed to investigate the potential consequences of the impact of testing strategy. The model exhibits global dynamics concerning the disease-free and a unique endemic equilibrium depending on the basic reproduction number when the recruitment of infected individuals is zero; otherwise, the model does not have a disease-free equilibrium, and disease never dies out in the community. Model parameters have been estimated using the maximum likelihood method with respect to the data of early COVID-19 outbreak in India. The practical identifiability analysis shows that the model parameters are estimated uniquely. The consequences of the testing rate for the weekly new cases of early COVID-19 data in India tell that if the testing rate is increased by 20% and 30% from its baseline value, the weekly new cases at the peak are decreased by 37.63% and 52.90%; and it also delayed the peak time by four and fourteen weeks, respectively. Similar findings are obtained for the testing efficacy that if it is increased by 12.67% from its baseline value, the weekly new cases at the peak are decreased by 59.05% and delayed the peak by 15 weeks. Therefore, a higher testing rate and efficacy reduce the disease burden by tumbling the new cases, representing a real scenario. It is also obtained that the testing rate and efficacy reduce the epidemic's severity by increasing the final size of the susceptible population. The testing rate is found more significant if testing efficacy is high. Global sensitivity analysis using partial rank correlation coefficients (PRCCs) and Latin hypercube sampling (LHS) determine the key parameters that must be targeted to worsen/contain the epidemic.

Application of Artificial Intelligence-Based Regression Methods in the Problem of COVID-19 Spread Prediction: A Systematic Review

COVID-19 is one of the greatest challenges humanity has faced recently, forcing a change in the daily lives of billions of people worldwide. Therefore, many efforts have been made by researchers across the globe in the attempt of determining the models of COVID-19 spread. The objectives of this review are to analyze some of the open-access datasets mostly used in research in the field of COVID-19 regression modeling as well as present current literature based on Artificial Intelligence (AI) methods for regression tasks, like disease spread. Moreover, we discuss the applicability of Machine Learning (ML) and Evolutionary Computing (EC) methods that have focused on regressing epidemiology curves of COVID-19, and provide an overview of the usefulness of existing models in specific areas. An electronic literature search of the various databases was conducted to develop a comprehensive review of the latest AI-based approaches for modeling the spread of COVID-19. Finally, a conclusion is drawn from the observation of reviewed papers that AI-based algorithms have a clear application in COVID-19 epidemiological spread modeling and may be a crucial tool in the combat against coming pandemics.

A Diffusive Sveir Epidemic Model with Time Delay and General Incidence

In this paper, we consider a delayed diffusive SVEIR model with general incidence. We first establish the threshold dynamics of this model. Using a Nonstandard Finite Difference (NSFD) scheme, we then give the discretization of the continuous model. Applying Lyapunov functions, global stability of the equilibria are established. Numerical simulations are presented to validate the obtained results. The prolonged time delay can lead to the elimination of the infectiousness.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary material is available in the online version of this article at 10.1007/s10473-021-0421-9.

STEM: An Open Source Tool for Disease Modeling

The Spatiotemporal Epidemiologic Modeler (STEM) is an open source software project supported by the Eclipse Foundation and used by a global community of researchers and public health officials working to track and, when possible, control outbreaks of infectious disease in human and animal populations. STEM is not a model or a tool designed for a specific disease; it is a flexible, modular framework supporting exchange and integration of community models, reusable plug-in components, and denominator data, available to researchers worldwide at www.eclipse.org/stem. A review of multiple projects illustrates its capabilities. STEM has been used to study variations in transmission of seasonal influenza in Israel by strains; evaluate social distancing measures taken to curb the H1N1 epidemic in Mexico City; study measles outbreaks in part of London and inform local policy on immunization; and gain insights into H7N9 avian influenza transmission in China. A multistrain dengue fever model explored the roles of the mosquito vector, cross-strain immunity, and antibody response in the frequency of dengue outbreaks. STEM has also been used to study the impact of variations in climate on malaria incidence. During the Ebola epidemic, a weekly conference call supported the global modeling community; subsequent work modeled the impact of behavioral change and tested disease reintroduction via animal reservoirs. Work in Germany tracked salmonella in pork from farm to fork; and a recent doctoral dissertation used the air travel feature to compare the potential threats posed by weaponizing infectious diseases. Current projects include work in Great Britain to evaluate control strategies for parasitic disease in sheep, and in Germany and Hungary, to validate the model and inform policy decisions for African swine fever. STEM Version 4.0.0, released in early 2019, includes tools used in these projects and updates technical aspects of the framework to ease its use and re-use.

The Spatiotemporal Epidemiologic Modeler (STEM) is an open source software project supported by the Eclipse Foundation and used by a global community of researchers and public health officials working to track and, when possible, control outbreaks of infectious disease in human and animal populations. STEM is not a model or a tool designed for a specific disease; it is a flexible, modular framework supporting exchange and integration of community models, reusable plug‐in components, and denominator data, available to researchers worldwide.

Modelling the outbreak of infectious disease following mutation from a non-transmissible strain

In-host mutation of a cross-species infectious disease to a form that is transmissible between humans has resulted with devastating global pandemics in the past. We use simple mathematical models to describe this process with the aim to better understand the emergence of an epidemic resulting from such a mutation and the extent of measures that are needed to control it. The feared outbreak of a human–human transmissible form of avian influenza leading to a global epidemic is the paradigm for this study. We extend the SIR approach to derive a deterministic and a stochastic formulation to describe the evolution of two classes of susceptible and infected states and a removed state, leading to a system of ordinary differential equations and a stochastic equivalent based on a Markov process. For the deterministic model, the contrasting timescale of the mutation process and disease infectiousness is exploited in two limits using asymptotic analysis in order to determine, in terms of the model parameters, necessary conditions for an epidemic to take place and timescales for the onset of the epidemic, the size and duration of the epidemic and the maximum level of the infected individuals at one time. Furthermore, the basic reproduction number R0 is determined from asymptotic analysis of a distinguished limit. Comparisons between the deterministic and stochastic model demonstrate that stochasticity has little effect on most aspects of an epidemic, but does have significant impact on its onset particularly for smaller populations and lower mutation rates for representatively large populations. The deterministic model is extended to investigate a range of quarantine and vaccination programmes, whereby in the two asymptotic limits analysed, quantitative estimates on the outcomes and effectiveness of these control measures are established.

AVIAN INFLUENZA A H7N9 VIRUS HAS BEEN ESTABLISHED IN CHINA

In March 2013, a novel avian-origin influenza A H7N9 virus was identified among human patients in China and a total of 124 human cases with 24 related deaths were confirmed by May 2013. From November 2013 to July 2017, H7N9 broke out four more times in China. A deterministic model is proposed to study the transmission dynamics of the avian influenza A H7N9 virus between wild and domestic birds and from birds to humans, and is applied to simulate the open data on numbers of the infected human cases and related deaths reported from March to May 2013 and from November 2013 to June 2014 by the Chinese Center for Disease Control and Prevention. The basic reproduction number [Formula: see text] is estimated and sensitivity analysis of [Formula: see text] in terms of model parameters is performed. Taking into account the fact that it broke out again from November 2014 to June 2015, from November 2015 to July 2016, and from October 2016 to July 2017, we believe that H7N9 virus has been well established in birds and will likely cause regular outbreaks in humans again in the future. Control measures for the future spread of H7N9 include (i) reducing the transmission opportunities between wild birds and domestic birds, (ii) closing or monitoring the retail live-poultry markets in the infected areas, and (iii) culling the infected domestic birds in the epidemic regions.

Efficacies of prevention and control measures applied during an outbreak in Southwest Madrid, Spain

Leishmaniasis is a vector-borne disease of worldwide distribution, currently present in 98 countries. Since late 2010, an unusual increase of human visceral and cutaneous leishmaniasis cases has been observed in the south-western Madrid region, totaling more than 600 cases until 2015. Some hosts, such as human, domestic dog and cat, rabbit (Oryctolagus cuniculus), and hare (Lepus granatensis), were found infected by the parasite of this disease in the area. Hares were described as the most important reservoir due to their higher prevalence, capacity to infect the vector, and presence of the same strains as in humans. Various measures were adopted to prevent and control the disease, and since 2013 there was a slight decline in the human sickness. We used a mathematical model to evaluate the efficacy of each measure in reducing the number of infected hosts. We identified in the present model that culling both hares and rabbits, without immediate reposition of the animals, was the best measure adopted, decreasing the proportion of all infected hosts. Particularly, culling hares was more efficacious than culling rabbits to reduce the proportion of infected individuals of all hosts. Likewise, lowering vector contact with hares highly influenced the reduction of the proportion of infected hosts. The reduction of the vector density per host in the park decreased the leishmaniasis incidence of hosts in the park and the urban areas. On the other hand, the reduction of the vector density per host of the urban area (humans, dogs and cats) decreased only their affected population, albeit at a higher proportion. The use of insecticide-impregnated collar and vaccination in dogs affected only the infected dogs' population. The parameters related to the vector contact with dog, cat or human do not present a high impact on the other hosts infected by Leishmania. In conclusion, the efficacy of each control strategy was determined, in order to direct future actions in this and in other similar outbreaks. The present mathematical model was able to reproduce the leishmaniasis dynamics in the Madrid outbreak, providing theoretical support based on successful experiences, such as the reduction of human cases in Southwest Madrid, Spain.

Optimal treatment strategy of an avian influenza model with latency

Avian influenza, caused by influenza A viruses, has received worldwide attention over recent years. In this study, we formulate a mathematical model for avian influenza that includes human–human transmission and incorporates the effects of infection latency and treatments. We investigate the essential dynamics of the model through an equilibrium analysis. Meanwhile, we explore effective treatment strategies to control avian influenza outbreaks using optimal control theory. Our results show that strategically deployed medical treatments can significantly reduce the numbers of exposed and infection persons.

Competition between low and high pathogenicity avian influenza in a two-patch system

Over the last decade, the epidemiology of avian influenza has undergone a significant transformation. Not only have we seen an increase in the number of outbreaks of the deadly strain known as highly pathogenic avian influenza (HPAI), but the number of birds infected, and the cost of control has risen drastically. Live poultry markets play a huge role in the bird to bird transmission of avian influenza. We develop a two patch model to determine the competition between low pathogenic avian influenza (LPAI) and HPAI strains when migration is present. We define the two patches as live poultry markets in which the patches are connected through migration. We use a system of differential equations to analyze the existence-stability of the LPAI and HPAI equilibria and established results for the critical threshold R₀. We observed that in general migration in both directions increases the abundance of poultry infected with the HPAI strain. Migration promotes the coexistence in Patch 2 while in Patch 1 the region of coexistence fluctuates when migration is active between both patches.

An avian-only Filippov model incorporating culling of both susceptible and infected birds in combating avian influenza

Depopulation of birds has always been an effective method not only to control the transmission of avian influenza in bird populations but also to eliminate influenza viruses. We introduce a Filippov avian-only model with culling of susceptible and/or infected birds. For each susceptible threshold level [Formula: see text], we derive the phase portrait for the dynamical system as we vary the infected threshold level [Formula: see text], focusing on the existence of endemic states; the endemic states are represented by real equilibria, pseudoequilibria and pseudo-attractors. We show generically that all solutions of this model will approach one of the endemic states. Our results suggest that the spread of avian influenza in bird populations is tolerable if the trajectories converge to the equilibrium point that lies in the region below the threshold level [Formula: see text] or if they converge to one of the pseudoequilibria or a pseudo-attractor on the surface of discontinuity. However, we have to cull birds whenever the solution of this model converges to an equilibrium point that lies in the region above the threshold level [Formula: see text] in order to control the outbreak. Hence a good threshold policy is required to combat bird flu successfully and to prevent overkilling birds.

Global threshold dynamics of an SIVS model with waning vaccine-induced immunity and nonlinear incidence

Vaccination is the most effective method of preventing the spread of infectious diseases. For many diseases, vaccine-induced immunity is not life long and the duration of immunity is not always fixed. In this paper, we propose an SIVS model taking the waning of vaccine-induced immunity and general nonlinear incidence into consideration. Our analysis shows that the model exhibits global threshold dynamics in the sense that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable implying the disease dies out; while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable indicating that the disease persists. This global threshold result indicates that if the vaccination coverage rate is below a critical value, then the disease always persists and only if the vaccination coverage rate is above the critical value, the disease can be eradicated.