How Large Fraction of A Population Must be Vaccinated before A Disease is Controlled?

The ongoing Covid-19 pandemic has already caused more than 5 million casualties despite hard restrictions and relatively high vaccine coverage in many countries. The crucial question is therefore, how large vaccination rate and how severe restrictions are required to terminate the spread of the decease, assuming that the vaccine efficiency and the basic reproduction ratio (R0) are known? To answer this question, a mathematical equation was applied to visualize the required vaccination level as function of vaccine efficiency, restriction efficiency and basic reproduction ratio (R0). In addition to the modelling study, Covid-19 data from Europe was collected during 19/11-26/11 (2021) to assess the relation between vaccination rate and incidence. The analysis indicates that a vaccination rate of ~92% (2 doses) is required to stop Delta (B.1.617.2) without severe restrictions, under conditions like those in Europe late November 2021. A third vaccine dose, improved vaccines, higher vaccination rates and/or stronger restrictions will be required to force Omicron (B.1.1.529) to expire without infecting a large fraction of the population.

How Large Fraction of A Population Must be Vaccinated before A Disease is Controlled?

The ongoing Covid-19 pandemic has already caused more than 5 million casualties despite hard restrictions and relatively high vaccine coverage in many countries. The crucial question is therefore, how large vaccination rate and how severe restrictions are required to terminate the spread of the decease, assuming that the vaccine efficiency and the basic reproduction ratio (R0) are known? To answer this question, a simple mathematical equation was developed to visualize the required vaccination level as function of vaccine efficiency, restriction efficiency and basic reproduction ratio (R0). In addition to the modelling study, Covid-19 data from Europe was collected during 19/11-26/11 (2021) to assess the relation between vaccination rate and incidence. The analysis indicates that a vaccination rate of ~92% (2 doses) is currently required to stop Delta (B.1.617.2) without severe restrictions, using the vaccines that are most common in Europe today. A third vaccine dose, improved vaccines, higher vaccination rates and/or stronger restrictions will be required to force Omicron (B.1.1.529) to expire without infecting a large fraction of the population.

Analysis of A Coendemic Model of COVID-19 and Dengue Disease

The coronavirus disease 2019 (COVID-19) pandemic continues to spread aggressively worldwide, infecting more than 170 million people with confirmed cases, including more than 3 million deaths. This pandemic is increasingly exacerbating the burden on tropical and subtropical regions of the world due to the pre-existing dengue fever, which has become endemic for a longer period in the same region. Co-circulation dengue and COVID-19 cases have been found and confirmed in several countries. In this paper, a deterministic model for the coendemic of COVID-19 and dengue is proposed. The basic reproduction ratio is obtained, which is related to the four equilibria, disease-free, endemic-COVID-19, endemic-dengue, and coendemic equilibria. Stability analysis is done for the first three equilibria. Furthermore, a condition for coexistence equilibrium is obtained, which gives a condition for bifurcation analysis. Numerical simulations were carried out to obtain a stable limit-cycle resulting from two Hopf bifurcation points with dengue transmission rate and COVID-19 transmission rate as the bifurcation parameter, representing a stable periodic coexistence of dengue and COVID-19 transmission. We identify the period of limit cycle decreases after reaching the maximum value.

Prediction of COVID-19 evolution in Binh Duong province using SIR epidemiological model

With the fast growth of the COVID-19 pandemic, in-silico studies based on the susceptible-infected-removed (SIR) epidemiological model are very critical to provide reliable predictions of the COVID-19 evolution that can effectively support governments to issue the right measures to prevent and control the pandemic. In this study, the evolution of the COVID-19 in the Binh Duong province is investigated using the SIR model implemented in R-Studio software, in which the homemade computer codes based on the SIR model are developed using R language to automatically detect the optimal parameters in the model, including the reproduction ratio R0, the infection coefficient β, and the recovery coefficient γ. The SIR predictions indicate that the number of new positive cases per day in the Binh Duong province is only 40 new cases by November 30, 2021, and the total number of new cases per day becomes zero by middle February 2021. Besides, the Binh Duong province only has 1126 infected cases by November 30, 2021, which reduces to 203 cases at the end of December 2021. Through the SIR results, the COVID-19 pandemic in the Binh Duong is predicted to be ended at the end of December 2021.

Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations

This paper deals with the stochastic Zika virus model within the human and mosquito population. Firstly, we prove that there exists a global positive solution. Further, we found the condition for a viral infection to be extinct. Besides that, we discuss the existence of a unique ergodic stationary distribution through a suitable Lyapunov function. The stationary distribution validates the occurrence of infection in the population. From that, we obtain the threshold value for prevail and disappear of disease within the population. Through the numerical simulations, we have verified the reproduction ratio R 0 S ${R}_{0}^{S}$ as stated in our theoretical findings.

ENGINEERING MATHEMATICAL MODELLING OF CORONA VIRUS (COVID-19) TRANSMISSION IN IRAQ

Purpose: As a result of a sudden spreading of an epidemic novel virus, scientifically named COVID-19, this paper has been done to present a contribution towards fighting this virus in Iraq. Methodology: This investigation is focusing on constructing an engineering mathematical model based on the Suspected, Infected, and Recovered model (SIR), given by Kermack and McKendrick. Main Findings: Iraqi people are facing and suffering from this COVID-19. Three governorates occupying the locally highest infection levels, plus the world's highest deaths to infected cases ratio of about 11%, are Baghdad, Sulaimani, and Karbala. Implications: It is showed that the Reproduction ratio R0)K is positive (greater than 1) in the three nominated zones, which means that the epidemic disease will keep spreading in a broad manner and depending on many specific factors. Many effective recommendations are presented to avoid spreading this novel virus via many techniques. Novelty: SIR model is used to assess epidemic levels in 3 zones.

The introduction of a mandatory mask policy was associated with significantly reduced COVID-19 cases in a major metropolitan city

Background Whilst evidence of use of face masks in reducing COVID-19 cases is increasing, the impact of mandatory use across a large population has been difficult to assess. Introduction of mandatory mask use on July 22, 2020 during a resurgence of COVID-19 in Melbourne, Australia created a situation that facilitated an assessment of the impact of the policy on the epidemic growth rate as its introduction occurred in the absence of other changes to restrictions. Methods and findings Exponential epidemic growth or decay rates in daily COVID-19 diagnoses were estimated using a non-weighted linear regression of the natural logarithm of the daily cases against time, using a linear spline model with one knot (lspline package in R v 3.6.3). The model’s two linear segments pivot around the hinge day, on which the mask policy began to take effect, 8 days following the introduction of the policy. We used two forms of data to assess change in mask usage: images of people wearing masks in public places obtained from a major media outlet and population-based survey data. Potential confounding factors (including daily COVID-19 tests, number of COVID-19 cases among population subsets affected differentially by the mask policy–e.g., healthcare workers) were examined for their impact on the results. Daily cases fitted an exponential growth in the first log-linear segment (k = +0.042, s.e. = 0.007), and fitted an exponential decay in the second (k = -0.023, s.e. = 0.017) log-linear segment. Over a range of reported serial intervals for SARS-CoV-2 infection, these growth rates correspond to a 22–33% reduction in an effective reproduction ratio before and after mandatory mask use. Analysis of images of people in public spaces showed mask usage rose from approximately 43% to 97%. Analysis of survey data found that on the third day before policy introduction, 44% of participants reported “often” or “always” wearing a mask; on the fourth day after, 100% reported “always” doing so. No potentially confounding factors were associated with the observed change in growth rates. Conclusions The mandatory mask use policy substantially increased public use of masks and was associated with a significant decline in new COVID-19 cases after introduction of the policy. This study strongly supports the use of masks for controlling epidemics in the broader community.

Critical fluctuations in epidemic models explain COVID-19 post-lockdown dynamics

As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves, even when the community disease transmission rate $$\beta$$ β is not significantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, $$\beta > \beta _c$$ β > β c ) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, $$\beta < \beta _c$$ β < β c ) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with $$r(t) \approx 1$$ r ( t ) ≈ 1 hovering around its threshold value.

Vaccine escape in a heterogeneous population: insights for SARS-CoV-2 from a simple model

As a countermeasure to the SARS-CoV-2 pandemic, there has been swift development and clinical trial assessment of candidate vaccines, with subsequent deployment as part of mass vaccination campaigns. However, the SARS-CoV-2 virus has demonstrated the ability to mutate and develop variants, which can modify epidemiological properties and potentially also the effectiveness of vaccines. The widespread deployment of highly effective vaccines may rapidly exert selection pressure on the SARS-CoV-2 virus directed towards mutations that escape the vaccine-induced immune response. This is particularly concerning while infection is widespread. By developing and analysing a mathematical model of two population groupings with differing vulnerability and contact rates, we explore the impact of the deployment of vaccines among the population on the reproduction ratio, cases, disease abundance and vaccine escape pressure. The results from this model illustrate two insights: (i) vaccination aimed at reducing prevalence could be more effective at reducing disease than directly vaccinating the vulnerable; (ii) the highest risk for vaccine escape can occur at intermediate levels of vaccination. This work demonstrates a key principle: the careful targeting of vaccines towards particular population groups could reduce disease as much as possible while limiting the risk of vaccine escape.