An age-of-infection model with both symptomatic and asymptomatic infections.

We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number [Formula: see text] and establish the final size relation. It is shown that the ratio of accumulated counts of symptomatic patients and asymptomatic patients is determined by the symptomatic ratio f which is defined as the probability of eventually becoming symptomatic after being infected. We also formulate and study a general age-of-infection model with disease deaths and with two infection pathways. The final size relation is investigated, and the upper and lower bounds for final epidemic size are given. Several numerical simulations are performed to verify the analytical results.

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.

The importance of quarantine: modelling the COVID-19 testing process.

We incorporate the disease state and testing state into the formulation of a COVID-19 epidemic model. For this model, the basic reproduction number is identified and its dependence on model parameters related to the testing process and isolation efficacy is discussed. The relations between the basic reproduction number, the final epidemic and peak sizes, and the model parameters are further explored numerically. We find that fast test reporting does not always benefit the control of the COVID-19 epidemic if good quarantine while awaiting test results is implemented. Moreover, the final epidemic and peak sizes do not always increase along with the basic reproduction number. Under some circumstances, lowering the basic reproduction number increases the final epidemic and peak sizes. Our findings suggest that properly implementing isolation for individuals who are waiting for their testing results would lower the basic reproduction number as well as the final epidemic and peak sizes.

Modeling COVID-19 dynamics in the sixteen West African countries.

The COVID-19 pandemic is currently causing several damages to the world, especially in the public health sector. Due to identifiability problems in parameters' estimation of complex compartmental models, this study considered a simple deterministic susceptible-infectious-recovered (SIR)-type model to characterize the first wave and predict the future course of the pandemic in the West African countries. We estimated some specific characteristics of the disease's dynamics, such as its initial conditions, reproduction numbers, true peak and peak of the reported cases, with their corresponding times, final epidemic size and time-varying attack ratio. Our findings revealed a relatively low proportion of susceptible individuals in the region and the different countries ( 1.2 % across West Africa). The detection rate of the disease was also relatively low ( 0.9 % for West Africa as a whole) and < 2 % for most countries, except for Gambia (12.5 %), Cape-Verde ( 9.5 % ), Mauritania ( 5.9 % ) and Ghana ( 4.4 % ). The reproduction number varied between 1.15 (Burkina-Faso) and 4.45 (Niger), and most countries' peak time of the first wave of the pandemic was between June and July. Generally, the peak time of the reported cases came a week (7-8 days) after the true peak time. The model predicted for the first wave, 222,100 actual active cases in the region at the peak time, while the final epidemic size accounted for 0.6 % of the West African population (2,526,700 individuals). The results showed that COVID-19 has not severely affected West Africa as in other regions. However, current control measures and standard operating procedures should be maintained over time to accelerate a decline in the observed trends of the pandemic.

Effect of Non-homogeneous Mixing and Asymptomatic Individuals on Final Epidemic Size and Basic Reproduction Number in a Meta-Population Model.

To uncover the effective interventions during the pandemic period, a novel mathematical model, which incorporates separate compartments for incubation and asymptomatic individuals, has been developed in this paper. On the basis of a general mixing, final size relation and next-generation matrix are derived for a meta-population model by introducing the matrix blocking. The final size ([Formula: see text]) and the basic reproduction number ([Formula: see text]) are no longer a simple monotonous relationship. The analytical results of heterogeneity illustrate that activity is more sensitive than the others. And the proportion of asymptomatic individuals is a key factor for final epidemic size compared to the regulatory factor. Furthermore, the impact of preferential contact level on [Formula: see text] and [Formula: see text] is comparatively complex. The isolation can effectively reduce the final size, which further verifies its effectiveness. When vaccination is considered, the mixing methods maybe influence the doses of vaccination used and its effective. Moreover, using the present predictive model, we can provide the valuable reference about identifying the ideal strategies to curb the pandemic disease.

The Effect of Face Mask Use on COVID-19 Models.

We begin with a simple model for the COVID-19 epidemic and add face mask usages and testing and quarantine of infectives. We estimate the effect on the reproduction number and discuss the question of whether the epidemic can be controlled by increased use of face masks.

Imitation dynamics in the mitigation of the novel coronavirus disease (COVID-19) outbreak in Wuhan, China from 2019 to 2020.

BACKGROUND: The coronavirus disease 2019 (COVID-19) was first identified in Wuhan, China on December 2019 in patients presenting with atypical pneumonia. Although 'city-lockdown' policy reduced the spatial spreading of the COVID-19, the city-level outbreaks within each city remain a major concern to be addressed. The local or regional level disease control mainly depends on individuals self-administered infection prevention actions. The contradiction between choice of taking infection prevention actions or not makes the elimination difficult under a voluntary acting scheme, and represents a clash between the optimal choice of action for the individual interest and group interests. METHODS: We develop a compartmental epidemic model based on the classic susceptible-exposed-infectious-recovered model and use this to fit the data. Behavioral imitation through a game theoretical decision-making process is incorporated to study and project the dynamics of the COVID-19 outbreak in Wuhan, China. By varying the key model parameters, we explore the probable course of the outbreak in terms of size and timing under several public interventions in improving public awareness and sensitivity to the infection risk as well as their potential impact. RESULTS: We estimate the basic reproduction number, R 0, to be 2.5 (95% CI: 2.4-2.7). Under the current most realistic setting, we estimate the peak size at 0.28 (95% CI: 0.24-0.32) infections per 1,000 population. In Wuhan, the final size of the outbreak is likely to infect 1.35% (95% CI: 1.00-2.12%) of the population. The outbreak will be most likely to peak in the first half of February and drop to daily incidences lower than 10 in June 2020. Increasing sensitivity to take infection prevention actions and the effectiveness of infection prevention measures are likely to mitigate the COVID-19 outbreak in Wuhan. CONCLUSIONS: Through an imitating social learning process, individual-level behavioral change on taking infection prevention actions have the potentials to significantly reduce the COVID-19 outbreak in terms of size and timing at city-level. Timely and substantially resources and supports for improving the willingness-to-act and conducts of self-administered infection prevention actions are recommended to reduce to the COVID-19 associated risks.