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1.
J Biol Dyn ; 16(1): 619-639, 2022 12.
Article in English | MEDLINE | ID: covidwho-2187649

ABSTRACT

In this paper, we are concerned with an epidemic model with quarantine and distributed time delay. We define the basic reproduction number R0 and show that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, then it is unstable and there exists a unique endemic equilibrium. We obtain sufficient conditions for a Hopf bifurcation that induces a nontrivial periodic solution which represents recurrent epidemic waves. By numerical simulations, we illustrate stability and instability parameter regions. Our results suggest that the quarantine and time delay play important roles in the occurrence of recurrent epidemic waves.


Subject(s)
Epidemics , Quarantine , Basic Reproduction Number , Computer Simulation , Models, Biological
2.
Sci Rep ; 12(1): 19435, 2022 Nov 13.
Article in English | MEDLINE | ID: covidwho-2119152

ABSTRACT

A mathematical model is presented in this paper to investigate the effects of time delay in vaccine production on COVID-19 spread. The model is analyzed qualitatively and numerically. The qualitative analysis indicates that the system variables are non-negative, bounded, and biologically meaningful. Moreover, the model has produced two equilibrium points: the free equilibrium point, which can exist without conditions, and the endemic equilibrium point, which can exist if the control reproduction number, [Formula: see text], is not less than one. In addition, the local stability of the equilibrium points is investigated and agrees with the numerical analysis results. Finally, a sensitivity analysis is conducted for [Formula: see text]. In particular, we examine the effect of the vaccine's time delay, vaccine rate, and vaccine efficiency on the model dynamics.


Subject(s)
COVID-19 , Humans , Basic Reproduction Number , Computer Simulation , COVID-19/prevention & control , Vaccination , Models, Theoretical , Models, Biological
3.
Bull Math Biol ; 84(12): 146, 2022 Nov 11.
Article in English | MEDLINE | ID: covidwho-2117226

ABSTRACT

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number [Formula: see text] for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and there exists at least one positive periodic solution when [Formula: see text]. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of [Formula: see text]. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.


Subject(s)
COVID-19 , Humans , Computer Simulation , COVID-19/epidemiology , Models, Biological , Mathematical Concepts , Basic Reproduction Number
4.
Math Biosci Eng ; 19(10): 10618-10636, 2022 07 26.
Article in English | MEDLINE | ID: covidwho-2110345

ABSTRACT

A stochastic SIRS epidemic model with vaccination is discussed. A new stochastic threshold $ R_0/ $ is determined. When the noise is very low ($ R_0/ < 1 $), the disease becomes extinct, and if $ R_0/ > 1 $, the disease persists. Furthermore, we show that the solution of the stochastic model oscillates around the endemic equilibrium point and the intensity of the fluctuation is proportional to the intensity of the white noise. Computer simulations are used to support our findings.


Subject(s)
Models, Biological , Systemic Inflammatory Response Syndrome , Computer Simulation , Humans , Incidence , Stochastic Processes , Vaccination
6.
Bull Math Biol ; 84(12): 144, 2022 11 05.
Article in English | MEDLINE | ID: covidwho-2102924

ABSTRACT

It is well known in the literature that human behavior can change as a reaction to disease observed in others, and that such behavioral changes can be an important factor in the spread of an epidemic. It has been noted that human behavioral traits in disease avoidance are under selection in the presence of infectious diseases. Here, we explore a complementary trend: the pathogen itself might experience a force of selection to become less "visible," or less "symptomatic," in the presence of such human behavioral trends. Using a stochastic SIR agent-based model, we investigated the co-evolution of two viral strains with cross-immunity, where the resident strain is symptomatic while the mutant strain is asymptomatic. We assumed that individuals exercised self-regulated social distancing (SD) behavior if one of their neighbors was infected with a symptomatic strain. We observed that the proportion of asymptomatic carriers increased over time with a stronger effect corresponding to higher levels of self-regulated SD. Adding mandated SD made the effect more significant, while the existence of a time-delay between the onset of infection and the change of behavior reduced the advantage of the asymptomatic strain. These results were consistent under random geometric networks, scale-free networks, and a synthetic network that represented the social behavior of the residents of New Orleans.


Subject(s)
Epidemics , Models, Biological , Humans , Mathematical Concepts
7.
Sci Rep ; 12(1): 18104, 2022 Oct 27.
Article in English | MEDLINE | ID: covidwho-2087286

ABSTRACT

Cross-transmission of information has a profound influence on the progress of science and technology and the discipline integration in the field of education. In this work, knowledge gained from the viral recombination and variation in COVID-19 transmission is applied to information transmission. Virus recombination and virus variation are similar to the crossing and information fusion phenomena in information transmission. An S2I4MR model with information crossing and variation is constructed. Then, the local and global asymptotic stabilities of the information-free equilibrium and information-existence equilibrium are analyzed. Additionally, the basic reproduction number [Formula: see text] of the model is calculated. As such, an optimal control strategy is hereby proposed to promote the cross-transmission of information and generate variant information. The numerical simulations support the results of the theoretical analysis and the sensitivity of the system towards certain control parameters. In particular, the results show that strengthening information crossing promotes the generation of variant information. Furthermore, encouraging information exchange and enhancing education improve the generation of information crossing and information variation.


Subject(s)
COVID-19 , Humans , Basic Reproduction Number , Models, Biological
8.
Theory Biosci ; 141(4): 365-374, 2022 Nov.
Article in English | MEDLINE | ID: covidwho-2048564

ABSTRACT

In this paper, a new mathematical model that describes the dynamics of the within-host COVID-19 epidemic is formulated. We show the stochastic dynamics of Target-Latent-Infected-Virus free within the human body with discrete delay and noise. Positivity and uniqueness of the solutions are established. Our study shows the extinction and persistence of the disease inside the human body through the stability analysis of the disease-free equilibrium [Formula: see text] and the endemic equilibrium [Formula: see text], respectively. Moreover, we show the impact of delay tactics and noise on the extinction of the disease. The most interesting result is even if the deterministic system is inevitably pandemic at a specific point, extinction will become possible in the stochastic version of our model.


Subject(s)
COVID-19 , Epidemics , Humans , Models, Biological , SARS-CoV-2 , Models, Theoretical , Stochastic Processes , Computer Simulation
9.
J Math Biol ; 85(4): 43, 2022 09 28.
Article in English | MEDLINE | ID: covidwho-2048224

ABSTRACT

We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual's infection age, i.e., the time elapsed since infection, has three benefits. First, regardless of the number of types, the age distribution of the population can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. The frequency of type i is simply obtained by integrating the probability of being in state i at a given age against the age distribution. This representation induces a simple methodology based on the additional assumption of Poisson sampling to infer and forecast the epidemic. We illustrate this technique using French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual.


Subject(s)
COVID-19 , Epidemics , COVID-19/epidemiology , Forecasting , Humans , Models, Biological , Probability
10.
Sci Rep ; 12(1): 15688, 2022 09 20.
Article in English | MEDLINE | ID: covidwho-2036895

ABSTRACT

An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics-the World, Israel, The United States of America, and Japan.


Subject(s)
COVID-19 , COVID-19/epidemiology , COVID-19/prevention & control , Disease Susceptibility/epidemiology , Epidemiological Models , Humans , Models, Biological , Pandemics/prevention & control , Vaccination/methods
11.
Bull Math Biol ; 84(11): 122, 2022 09 17.
Article in English | MEDLINE | ID: covidwho-2035260

ABSTRACT

A dynamic model called SqEAIIR for the COVID-19 epidemic is investigated with the effects of vaccination, quarantine and precaution promotion when the traveling and immigrating individuals are considered as unknown disturbances. By utilizing only daily sampling data of isolated symptomatic individuals collected by Mexican government agents, an equivalent model is established by an adaptive fuzzy-rules network with the proposed learning law to guarantee the convergence of the model's error. Thereafter, the optimal controller is developed to determine the adequate intervention policy. The main theorem is conducted to demonstrate the setting of all designed parameters regarding the closed-loop performance. The numerical systems validate the efficiency of the proposed scheme to control the epidemic and prevent the overflow of requiring healthcare facilities. Moreover, the sufficient performance of the proposed scheme is achieved with the effect of traveling and immigrating individuals.


Subject(s)
COVID-19 , Quarantine , Algorithms , COVID-19/epidemiology , COVID-19/prevention & control , Computer Simulation , Feedback , Humans , Mathematical Concepts , Models, Biological , Neural Networks, Computer , Nonlinear Dynamics , Policy
12.
Bull Math Biol ; 84(11): 127, 2022 09 22.
Article in English | MEDLINE | ID: covidwho-2035259

ABSTRACT

Mathematical modeling is a tool used for understanding diseases dynamics. The discrete-time model is an especial case in modeling that satisfactorily describes the epidemiological dynamics because of the discrete nature of the real data. However, discrete models reduce their descriptive and fitting potential because of assuming a homogeneous population. Thus, in this paper, we proposed contagion probability functions according to two infection paradigms that consider factors associated with transmission dynamics. For example, we introduced probabilities of establishing an infectious interaction, the number of contacts with infectious and the level of connectivity or social distance within populations. Through the probabilities design, we overcame the homogeneity assumption. Also, we evaluated the proposed probabilities through their introduction into discrete-time models for two diseases and different study zones with real data, COVID-19 for Germany and South Korea, and dengue for Colombia. Also, we described the oscillatory dynamics for the last one using the contagion probabilities alongside parameters with a biological sense. Finally, we highlight the implementation of the proposed probabilities would improve the simulation of the public policy effect of control strategies over an infectious disease outbreak.


Subject(s)
COVID-19 , Models, Biological , COVID-19/epidemiology , Computer Simulation , Humans , Likelihood Functions , Mathematical Concepts , Probability
13.
J Biol Dyn ; 16(1): 665-712, 2022 Dec.
Article in English | MEDLINE | ID: covidwho-2028933

ABSTRACT

In this paper we assess the effectiveness of different non-pharmaceutical interventions (NPIs) against COVID-19 utilizing a compartmental model. The local asymptotic stability of equilibria (disease-free and endemic) in terms of the basic reproduction number have been determined. We find that the system undergoes a backward bifurcation in the case of imperfect quarantine. The parameters of the model have been estimated from the total confirmed cases of COVID-19 in India. Sensitivity analysis of the basic reproduction number has been performed. The findings also suggest that effectiveness of face masks plays a significant role in reducing the COVID-19 prevalence in India. Optimal control problem with several control strategies has been investigated. We find that the intervention strategies including implementation of lockdown, social distancing, and awareness only, has the highest cost-effectiveness in controlling the infection. This combined strategy also has the least value of average cost-effectiveness ratio (ACER) and associated cost.


Subject(s)
COVID-19 , Basic Reproduction Number , COVID-19/epidemiology , Communicable Disease Control , Cost-Benefit Analysis , Humans , Models, Biological
14.
Bull Math Biol ; 84(10): 116, 2022 09 10.
Article in English | MEDLINE | ID: covidwho-2014405

ABSTRACT

COVID-19 is caused by the SARS-CoV-2 virus, which is mainly transmitted directly between humans. However, it is observed that this disease can also be transmitted through an indirect route via environmental fomites. The development of appropriate and effective vaccines has allowed us to target and anticipate herd immunity. Understanding of the transmission dynamics and the persistence of the virus on environmental fomites and their resistive role on indirect transmission of the virus is an important scientific and public health challenge because it is essential to consider all possible transmission routes and route specific transmission strength to accurately quantify the herd immunity threshold. In this paper, we present a mathematical model that considers both direct and indirect transmission modes. Our analysis focuses on establishing the disease invasion threshold, investigating its sensitivity to both transmission routes and isolate route-specific transmission rate. Using the tau-leap algorithm, we perform a stochastic model simulation to address the invasion potential of both transmission routes. Our analysis shows that direct transmission has a higher invasion potential than that of the indirect transmission. As a proof of this concept, we fitted our model with early epidemic data from several countries to uniquely estimate the reproduction numbers associated with direct and indirect transmission upon confirming the identifiability of the parameters. As the indirect transmission possess lower invasion potential than direct transmission, proper estimation and necessary steps toward mitigating it would help reduce vaccination requirement.


Subject(s)
COVID-19 , Immunity, Herd , COVID-19/prevention & control , Humans , Mathematical Concepts , Models, Biological , SARS-CoV-2
15.
Bull Math Biol ; 84(10): 108, 2022 08 27.
Article in English | MEDLINE | ID: covidwho-2014404

ABSTRACT

As the availability of COVID-19 vaccines, it is badly needed to develop vaccination guidelines to prioritize the vaccination delivery in order to effectively stop COVID-19 epidemic and minimize the loss. We evaluated the effect of age-specific vaccination strategies on the number of infections and deaths using an SEIR model, considering the age structure and social contact patterns for different age groups for each of different countries. In general, the vaccination priority should be given to those younger people who are active in social contacts to minimize the number of infections, while the vaccination priority should be given to the elderly to minimize the number of deaths. But this principle may not always apply when the interaction of age structure and age-specific social contact patterns is complicated. Partially reopening schools, workplaces or households, the vaccination priority may need to be adjusted accordingly. Prematurely reopening social contacts could initiate a new outbreak or even a new pandemic out of control if the vaccination rate and the detection rate are not high enough. Our result suggests that it requires at least nine months of vaccination (with a high vaccination rate > 0.1%) for Italy and India before fully reopening social contacts in order to avoid a new pandemic.


Subject(s)
COVID-19 , Age Factors , Aged , COVID-19 Vaccines , Humans , Mathematical Concepts , Models, Biological , Policy , Vaccination
16.
Bull Math Biol ; 84(10): 106, 2022 08 25.
Article in English | MEDLINE | ID: covidwho-2014403

ABSTRACT

COVID-19 epidemics exhibited multiple waves regionally and globally since 2020. It is important to understand the insight and underlying mechanisms of the multiple waves of COVID-19 epidemics in order to design more efficient non-pharmaceutical interventions (NPIs) and vaccination strategies to prevent future waves. We propose a multi-scale model by linking the behaviour change dynamics to the disease transmission dynamics to investigate the effect of behaviour dynamics on COVID-19 epidemics using game theory. The proposed multi-scale models are calibrated and key parameters related to disease transmission dynamics and behavioural dynamics with/without vaccination are estimated based on COVID-19 epidemic data (daily reported cases and cumulative deaths) and vaccination data. Our modeling results demonstrate that the feedback loop between behaviour changes and COVID-19 transmission dynamics plays an essential role in inducing multiple epidemic waves. We find that the long period of high-prevalence or persistent deterioration of COVID-19 epidemics could drive almost all of the population to change their behaviours and maintain the altered behaviours. However, the effect of behaviour changes fades out gradually along the progress of epidemics. This suggests that it is essential to have not only persistent, but also effective behaviour changes in order to avoid subsequent epidemic waves. In addition, our model also suggests the importance to maintain the effective altered behaviours during the initial stage of vaccination, and to counteract relaxation of NPIs, it requires quick and massive vaccination to avoid future epidemic waves.


Subject(s)
COVID-19 , Epidemics , COVID-19/epidemiology , COVID-19/prevention & control , Epidemics/prevention & control , Game Theory , Humans , Mathematical Concepts , Models, Biological
17.
J Math Biol ; 85(3): 23, 2022 08 20.
Article in English | MEDLINE | ID: covidwho-2014120

ABSTRACT

Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values [Formula: see text] and [Formula: see text] for the treatment rate r: (i) when [Formula: see text], the disease will disappear; (ii) when [Formula: see text], the disease will persist. In a changing environment, the infective population starts along the stable disease-free state (or an endemic state) and surprisingly continues tracking the unstable disease-free state (or a limit cycle) when the system crosses a bifurcation point, and eventually tends to the stable endemic state (or the stable disease-free state). This transient tracking of the unstable disease-free state when [Formula: see text] predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change.


Subject(s)
Disease Outbreaks , Systemic Inflammatory Response Syndrome , Humans , Incidence , Models, Biological
18.
J Math Biol ; 85(2): 17, 2022 08 01.
Article in English | MEDLINE | ID: covidwho-2014119

ABSTRACT

We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution was proved. We defined the basic reproduction number and investigated the threshold dynamics of the model, and discussed the asymptotic behavior and monotonicity of the basic reproduction number associated with the diffusion rate. The local and global Hopf bifurcation at the endemic steady state was investigated theoretically and numerically. There exists numerical cases showing that the larger the number of basic reproduction number, the smaller the final epidemic size. The meaningful conclusion generalizes the previous conclusion of ordinary differential equation.


Subject(s)
Epidemics , Models, Biological , Basic Reproduction Number
19.
Proc Natl Acad Sci U S A ; 119(37): e2205598119, 2022 09 13.
Article in English | MEDLINE | ID: covidwho-2008361

ABSTRACT

The humoral immune response, a key arm of adaptive immunity, consists of B cells and their products. Upon infection or vaccination, B cells undergo a Darwinian evolutionary process in germinal centers (GCs), resulting in the production of antibodies and memory B cells. We developed a computational model to study how humoral memory is recalled upon reinfection or booster vaccination. We find that upon reexposure to the same antigen, affinity-dependent selective expansion of available memory B cells outside GCs (extragerminal center compartments [EGCs]) results in a rapid response made up of the best available antibodies. Memory B cells that enter secondary GCs can undergo mutation and selection to generate even more potent responses over time, enabling greater protection upon subsequent exposure to the same antigen. GCs also generate a diverse pool of B cells, some with low antigen affinity. These results are consistent with our analyses of data from humans vaccinated with two doses of a COVID-19 vaccine. Our results further show that the diversity of memory B cells generated in GCs is critically important upon exposure to a variant antigen. Clones drawn from this diverse pool that cross-react with the variant are rapidly expanded in EGCs to provide the best protection possible while new secondary GCs generate a tailored response for the new variant. Based on a simple evolutionary model, we suggest that the complementary roles of EGC and GC processes we describe may have evolved in response to complex organisms being exposed to evolving pathogen families for millennia.


Subject(s)
Antigens , B-Lymphocytes , Immunity, Humoral , Immunologic Memory , Antigens/immunology , B-Lymphocytes/immunology , COVID-19/prevention & control , COVID-19 Vaccines/immunology , Computer Simulation , Germinal Center/immunology , Humans , Models, Biological
20.
Comput Methods Programs Biomed ; 225: 107094, 2022 Oct.
Article in English | MEDLINE | ID: covidwho-2007619

ABSTRACT

BACKGROUND AND OBJECTIVE: Pulmonary fibrosis (PF) is a chronic progressive disease with an extremely high mortality rate and is a complication of COVID-19. Inhalable microspheres have been increasingly used in the treatment of lung diseases such as PF in recent years. Compared to the direct inhalation of drugs, a larger particle size is required to ensure the sustained release of microspheres. However, the clinical symptoms of PF may lead to the easier deposition of microspheres in the upper respiratory tract. Therefore, it is necessary to understand the effects of PF on the deposition of microspheres in the respiratory tract. METHODS: In this study, airway models with different degrees of PF in humans and mice were established, and the transport and deposition of microspheres in the airway were simulated using computational fluid dynamics. RESULTS: The simulation results showed that PF increases microsphere deposition in the upper respiratory tract and decreases bronchial deposition in both humans and mice. Porous microspheres with low density can ensure deposition in the lower respiratory tract and larger particle size. In healthy and PF humans, porous microspheres of 10 µm with densities of 700 and 400 kg/m³ were deposited most in the bronchi. Unlike in humans, microspheres larger than 4 µm are completely deposited in the upper respiratory tract of mice owing to their high inhalation velocity. For healthy and PF mice, microspheres of 6 µm with densities of and 100 kg/m³ are recommended. CONCLUSIONS: The results showed that with the exacerbation of PF, it is more difficult for microsphere particles to deposit in the subsequent airway. In addition, there were significant differences in the deposition patterns among the different species. Therefore, it is necessary to process specific microspheres from different individuals. Our study can guide the processing of microspheres and achieve differentiated drug delivery in different subjects to maximize therapeutic effects.


Subject(s)
COVID-19 , Pulmonary Fibrosis , Animals , Computer Simulation , Delayed-Action Preparations , Humans , Lung , Mice , Microspheres , Models, Biological , Particle Size , Porosity , Pulmonary Fibrosis/drug therapy , Respiratory Aerosols and Droplets , Trachea
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