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Abstract This study presents a mathematical model incorporating both asymptomatic and symptomatic HIV-infected individuals to analyze the dynamics of HIV/AIDS. This expanded model offers a more comprehensive understanding of the epidemic’s spread. We calculate the basic reproduction number (R0) to quantify the virus’s transmission potential. To achieve accurate and robust simulations, we introduce the Nonstandard Finite Difference Scheme (NSFD). Compared to traditional methods like RK-4, NSFD offers improved dynamical consistency and numerical precision, leading to enhanced stability and efficiency in simulating infectious diseases like HIV/AIDS. Local and global stability analysis are performed using the Routh-Hurwitz method. The NSFD method effectively captures the dynamics of HIV propagation under various scenarios, providing valuable insights into HIV/AIDS progression. We demonstrate the superiority of the NSFD approach compared to existing methods, paving the way for further research in modeling viral infections.

Abstract The use of plastic is very widespread in the world and the spread of plastic waste has also reached the oceans. Observing marine debris is a serious threat to the management system of this pollution. Because it takes years to recycle the current wastes, while their amount increases every day. The importance of mathematical models for plastic waste management is that it provides a framework for understanding the dynamics of this waste in the ocean and helps to identify effective strategies for its management. A mathematical model consisting of three compartments plastic waste, marine debris, and recycle is studied in the form of a system of ordinary differential equations. After describing the formulation of the model, some properties of the model are given. Then the equilibria of the model and the basic reproduction number are obtained by the next generation matrix method. In addition, the global stability of the model are proved at the equilibria. The bifurcations of the model and sensitivity analysis are also used for better understanding of the dynamics of the model. Finally, the numerical simulations of discussed models are given and the model is examined in several aspects. It is proven that the solutions of the system are positive if initial values are positive. It is shown that there are two equilibria $$E^0$$ E 0 and $$E^*$$ E ∗ and if $${{\mathcal {B}}}{{\mathcal {R}}}1$$ B R > 1 , the equilibrium $$E^*$$ E ∗ exists and it is globally stable. Also, at $${{\mathcal {B}}}{{\mathcal {R}}}=1$$ B R = 1 the model exhibits a forward bifurcation. The sensitivity analysis of $${{\mathcal {B}}}{{\mathcal {R}}}$$ B R concludes that the rates of waste to marine, new waste, and the recycle rate have most effect on the amount of marine debris.

Abstract The Zika virus (ZIKV) is a serious global public health crisis. A major control challenge is its multiple transmission modes. This paper aims to simulate the transmission patterns of ZIKV using a dynamic process-based epidemiological model written in ordinary differential equations, which incorporates the human-to-mosquito infection by bites and sewage, mosquito-to-human infection by bites, and human-to-human infection by sex. Mathematical analyses are carried out to calculate the basic reproduction number and backward bifurcation, and prove the existence and stability of the equilibria. The model is validated with infection data by applying it to the 2015–2016 ZIKV epidemic in Brazil. The results indicate that the reproduction number is estimated to be 2.13, in which the contributions by mosquito bite, sex and sewage account for 85.7%, 3.5% and 10.8%, respectively. This number and the morbidity rate are most sensitive to parameters related to mosquito ecology, rather than asymptomatic or human-to-human transmission. Multiple transmission routes and suitable temperature exacerbate ZIKV infection in Brazil, and the vast majority of human infection cases were prevented by the intervention implemented. These findings may provide new insights to improve the risk assessment of ZIKV infection.

Abstract A mathematical model that describes the dynamics of bacterium vibrio cholera within a fixed population considering intrinsic bacteria growth, therapeutic treatment, sanitation and vaccination rates is developed. The developed mathematical model is validated against real cholera data. A sensitivity analysis of some of the model parameters is also conducted. The intervention rates are found to be very important parameters in reducing the values of the basic reproduction number. The existence and stability of equilibrium solutions to the mathematical model are also carried out using analytical methods. The effect of some model parameters on the stability of equilibrium solutions, number of infected individuals, number of susceptible individuals and bacteria density is rigorously analyzed. One very important finding of this research work is that keeping the vaccination rate fixed and varying the treatment and sanitation rates provide a rapid decline of infection. The fourth order Runge–Kutta numerical scheme is implemented in MATLAB to generate the numerical solutions.

Anthrax, a zoonotic disease affecting both livestock and humans globally, is caused by Bacillus anthracis. The objectives of this study were the following: (1) to identify environmental risk factors for anthrax and use this information to develop an improved predictive risk map, and (2) to estimate spatial variation in basic reproduction number (Ro) and herd immunity threshold at the village level, which can be used to optimize vaccination policies within high-risk regions. Based on the anthrax incidences from 2000–2023 and vaccine administration figures between 2008 and 2022 in Karnataka, this study depicted spatiotemporal pattern analysis to derive a risk map employing machine learning algorithms and estimate Ro and herd immunity threshold for better vaccination coverage. Risk factors considered were key meteorological, remote sensing, soil, and geographical parameters. Spatial autocorrelation and SaTScan analysis revealed the presence of hotspots and clusters predominantly in the southern, central, and uppermost northern districts of Karnataka and temporal cluster distribution between June and September. Factors significantly associated with anthrax were air temperature, surface pressure, land surface temperature (LST), enhanced vegetation index (EVI), potential evapotranspiration (PET), soil temperature, soil moisture, pH, available potassium, sulphur, and boron, elevation, and proximity to waterbodies and waterways. Ensemble technique with random forest and classification tree models were used to improve the prediction accuracy of anthrax. High-risk areas are expected in villages in the southern, central, and extreme northern districts of Karnataka. The estimated Ro revealed 11 high-risk districts with Ro > 1.50 and respective herd immunity thresholds ranging from 11.24% to 55.47%, and the assessment of vaccination coverage at the 70%, 80%, and 90% vaccine efficacy levels, all serving for need-based strategic vaccine allocation. A comparison analysis of vaccinations administered and vaccination coverage estimated in this study is used to illustrate difference in the supply and vaccine force. The findings from the present study may support in planning preventive interventions, resource allocation, especially of vaccines, and other control strategies against anthrax across Karnataka, specifically focusing on predicted high-risk regions.

Background: Since the early 1980s, human immunodeficiency virus (HIV) and its accompanying acquired immunodeficiency syndrome (AIDS) have spread worldwide, becoming one of the world's major global health issues. From the beginning of the epidemic until 2020, about 79.3 million people became infected, with 36.3 million deaths due to AIDS illnesses. This huge figure is a result of those unaware of their status due to stigmatization and invariably spreading the virus unknowingly. Methods: Qualitative analysis through a mathematical model that will address HIV unaware individuals and the effect of an increasing defaulter on the dynamics of HIV/AIDS was investigated. The impact of treatment and the effect of inefficient follow-up on the transmission of HIV/AIDS were examined. The threshold for the effective reduction of the unaware status of HIV through testing, in response to awareness, and the significance of effective non-defaulting in treatment commonly called defaulters loss to follow-up as these individuals contribute immensely to the spread of the virus due to their increase in CD4+ count was determined in this study. Stability analysis of equilibrium points is performed using the basic reproduction number $R_0$, an epidemiological threshold that determines disease eradication or persistence in viral populations. We tested the most sensitive parameters in the basic reproduction numbers. Results: The results portray that early identification and treatment only are inadequate for the illness to be eradicated, but effectively used of condom, strict adherence to treatment and counseling of and testing of pregnant women contribute to a decrease in infected HIV individuals. Conclusions: Other control techniques, such as treatment adherence and effective condom usage, and reduction in vertical transmission cannot be over-emphasis to lessen the disease's burden. Policymakers must address these strategies through a series of public awareness campaigns about the dangers of not adhering to treatment procedures and patterns.

Nigeria continues to record increasing number of persons infected with the coronavirus disease. Within the African region, Nigeria has the second-highest number of infected persons after South Africa, representing 9.95% of the region’s total coronavirus disease cases as at June 1, 2020, despite its strict containment measures. With the fears of a second wave of the coronavirus (the COVID-19 Delta Virus), another lockdown might likely be. But can we establish a correlation between infected persons and those prone to infection (susceptible) as well as the correlation strength in Nigeria? Using both a descriptive and econometric technique, the study analyzed the reality of the transmission rate and the rising figures of the coronavirus infections and found that there exists a weak correlation between the infected and the susceptible and that the basic reproduction number (R0) is less than 1 suggesting that the rate of transmission is low and the virus might not be endemic. The study, therefore, recommends that the containment measures of sanitizing/washing hands, physical distancing, and using face coverings are just enough to stem the tide. However, sustained lockdown measures will be too costly for the economy and a second lockdown will be highly unnecessary.

The monkeypox virus (MPXV) has caused an unusual epidemiological scenario—an epidemic within a pandemic (COVID-19). Despite the inherent evolutionary and adaptive capacity of poxviruses, one of the potential triggers for the emergence of this epidemic was the change in the status of orthopoxvirus vaccination and eradication programs. This epidemic outbreak of HMPX spread worldwide, with a notable frequency in Europe, North America, and South America. Due to these particularities, the objective of the present study was to assess and compare cases of HMPX in these geographical regions through logistic and Gompertz mathematical modeling over one year since its inception. We estimated the highest contagion rates (people per day) of 690, 230, 278, and 206 for the world, Europe, North America, and South America, respectively, in the logistic model. The equivalent values for the Gompertz model were 696, 268, 308, and 202 for the highest contagion rates. The Kruskal–Wallis Test indicated different means among the geographical regions affected by HMPX regarding case velocity, and the Wilcoxon pairwise test indicated the absence of significant differences between the case velocity means between Europe and South America. The coefficient of determination (R2) values in the logistic model varied from 0.8720 to 0.9023, and in the Gompertz model, they ranged from 0.9881 to 0.9988, indicating a better fit to the actual data when using the Gompertz model. The estimated basic reproduction numbers (R0) were more consistent in the logistic model, varying from 1.71 to 1.94 in the graphical method and from 1.75 to 1.95 in the analytical method. The comparative assessment of these mathematical modeling approaches permitted the establishment of the Gompertz model as the better-fitting model for the data and the logistic model for the R0. However, both models successfully represented the actual HMPX case data. The present study estimated relevant epidemiological data to understand better the geographic similarities and differences in the dynamics of HMPX.

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

Objectives. The analysis of transmission dynamics is crucial to determine whether mitigation or suppression measures reduce the spread of coronavirus disease 2019 (COVID-19). This study sought to estimate the basic (R0) and time-varying (Rt) reproduction number of COVID-19 and contrast the public health measures for ten South American countries. Methods. Data was obtained from the European Centre for Disease Prevention and Control. Country-specific R0 values during the first two weeks of the outbreak and Rt values after 90 days were estimated. Results. Countries used a combination of isolation, physical distancing, quarantine, and community-wide containment measures to staunch the spread of COVID-19 at different points in time. R0 ranged from 1.52 (95% confidence interval: 1.13-1.99) in Venezuela to 3.83 (3.04-4.75) in Chile, whereas Rt after 90 days ranged from 0.71 (95% credible interval: 0.39-1.05) in Uruguay to 1.20 (1.19-1.20) in Brazil. Different R0 and Rt values may be related to the testing capacity of each country. Conclusion. R0 in the early phase of the outbreak varied across the South American countries. The public health measures adopted in the initial period of the pandemic appear to have reduced Rt over time in each country, albeit to different levels.

Abstract Objective Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number $$R_0$$ R 0 . The model equations are solved numerically using fourth and fifth order Runge–Kutta methods. Results We found an $$R_0$$ R 0 of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus.

Abstract Objectives: The global incidence of HIV infection is not significantly decreasing, especially in sub-Saharan African countries. Though there is availability and accessibility of free HIV services, people are not being diagnosed early for HIV, and hence HIV-related mortality remains significantly high. We formulate a mathematical model for the spread of HIV using non linear ordinary differential equations in order to investigate the impact of late diagnosis of HIV on the spread of HIV. Results: The results suggest the need to encourage early initiation into HIV treatment as well as promoting HIV self-testing programs that enable more undiagnosed people to know their HIV status in order to curtail the continued spread of HIV.

Objectives The outbreak of coronavirus disease 2019 (COVID-19) is one of the main public health challenges currently facing the world. Because of its high transmissibility, COVID-19 has already caused extensive morbidity and mortality in many countries throughout the world. An accurate estimation of the basic reproduction number (R0) of COVID-19 would be beneficial for prevention programs. In light of discrepancies in original research on this issue, this systematic review and meta-analysis aimed to estimate the pooled R0 for COVID-19 in the current outbreak. Methods International databases (including Google Scholar, Science Direct, PubMed, and Scopus) were searched to identify studies conducted regarding the R0 of COVID-19. Articles were searched using the following keywords: “COVID-19” and “basic reproduction number” or “R0.” The heterogeneity among studies was assessed using the I2 index, the Cochran Q test, and T2. A random-effects model was used to estimate R0 in this study. Results The mean reported R0 in the identified articles was 3.38±1.40, with a range of 1.90 to 6.49. According to the results of the random-effects model, the pooled R0 for COVID-19 was estimated as 3.32 (95% confidence interval, 2.81 to 3.82). According to the results of the meta-regression analysis, the type of model used to estimate R0 did not have a significant effect on heterogeneity among studies (p=0.81). Conclusions Considering the estimated R0 for COVID-19, reducing the number of contacts within the population is a necessary step to control the epidemic. The estimated overall R0 was higher than the World Health Organization estimate.

The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China, which causes a severe and potentially fatal respiratory syndrome. Since then, it has been declared a pandemic by the World Health Organization and has spread around the globe. A reaction–diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process, in which different substances are transformed, and a diffusion process, which causes their distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic using the bias of reaction–diffusion equations. Both local and global asymptotic stability conditions for the equilibria were determined using a Lyapunov function, and the nature of the stability was determined using the Routh–Hurwitz criterion. Furthermore, we consider the conditions for the existence and uniqueness of the model solution and show the spatial distribution of the model compartments when the basic reproduction rate R0<1 and R0>1. Thereafter, we conducted a sensitivity analysis to determine the most sensitive parameters in the proposed model. We demonstrate the model’s effectiveness by performing numerical simulations and investigating the impact of vaccination, together with the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. Therefore, we offer to the public health policymakers a better understanding of COVID-19 management.

Varicella (chickenpox) is highly contagious among children and frequently breaks out in schools. In this study, we developed a dynamic compartment model to explore the optimal schedule for varicella vaccination in Jiangsu Province, China. A susceptible-infected-recovered (SIR) model was proposed to simulate the transmission of varicella in different age groups. The basic reproduction number was computed by the kinetic model, and the impact of three prevention factors was assessed through the global sensitivity analysis. Finally, the effect of various vaccination scenarios was qualitatively evaluated by numerical simulation. The estimated basic reproduction number was 1.831 ± 0.078, and the greatest contributor was the 5–10 year-old group (0.747 ± 0.042, 40.80%). Sensitivity analysis indicated that there was a strong negative correlation between the second dose vaccination coverage rate and basic reproduction number. In addition, we qualitatively found that the incidence would significantly decrease as the second dose vaccine coverage expands. The results suggest that two-dose varicella vaccination should be mandatory, and the optimal age of second dose vaccination is the 5–10 year-old group. Optimal vaccination time, wide vaccine coverage along with other measures, could enhance the effectiveness of prevention and control of varicella in China.

We estimated the weighted mean basic reproduction number (R0) of chikungunya virus based on outbreak size. R0 was 3.4 (95% CI 2.4–4.2) and varied for 2 primary chikungunya mosquito vectors: 4.1 (95% CI 1.5–6.6) for Aedes aegypti and 2.8 (95% CI 1.8–3.8) for Ae. albopictus.

Abstract Objectives We study the transmission dynamics of cholera in the presence of limited resources, a common feature of the developing world. The model is used to gain insight into the impact of available resources of the health care system on the spread and control of the disease. A deterministic model that includes a nonlinear recovery rate is formulated and rigorously analyzed. Limited treatment is described by inclusion of a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings. Results The model analysis shows that the disease free steady state is locally stable when the threshold $${\mathcal {R}}_{0} < 1$$ R0

Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses to viral infection. Immune response in COVID-19 infection can lead to longer recovery time and more severe secondary complications. We formulate a micro-level mathematical model by incorporating a saturation term for SARS-CoV-2-infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points have been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for R0<1, and endemic equilibrium exists and is globally stable for R0>1. Impulsive application of drug dosing has been applied for the treatment of COVID-19 patients. Additionally, the dynamics of the impulsive system are discussed when a patient takes drug holidays. Numerical simulations support the analytical findings and the dynamical regimes in the systems.

Background: Since the emergence of the COVID-19 pandemic, many models have been applied to understand its epidemiological characteristics. However, the ways in which outbreak data were used in some models are problematic, for example, importation was mixed up with local transmission. Methods: In this study, five models were proposed for the early Shaanxi outbreak in China. We demonstrated how to select a reasonable model and correctly use the outbreak data. Bayesian inference was used to obtain parameter estimates. Results: Model comparison showed that the renewal equation model generates the best model fitting and the Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) model is the worst; the performance of the SEEDAR model, which divides the exposure into two stages and includes the pre-symptomatic transmission, and SEEDDAAR model, which further divides infectious classes into two equally, lies in between. The Richards growth model is invalidated by its continuously increasing prediction. By separating continuous importation from local transmission, the basic reproduction number of COVID-19 in Shaanxi province ranges from 0.45 to 0.61, well below the unit, implying that timely interventions greatly limited contact between people and effectively contained the spread of COVID-19 in Shaanxi. Conclusions: The renewal equation model provides the best modelling; mixing continuous importation with local transmission significantly increases the estimate of transmissibility.

Abstract Background and aims Realizing the transmission potential and the magnitude of the coronavirus disease 2019 (COVID‐19) aids public health monitoring, strategies, and preparation. Two fundamental parameters, the basic reproduction number (R0) and case fatality rate (CFR) of COVID‐19, help in this understanding process. The objective of this study was to estimate the R0 and CFR of COVID‐19 and assess whether the parameters vary in different regions of the world. Methods We carried out a systematic review to find the reported estimates of the R0 and the CFR in articles from international databases between January 1 and August 31, 2020. Random‐effect models and Forest plots were implemented to evaluate the mean effect size of R0 and the CFR. Furthermore, R0 and CFR of the studies were quantified based on geographic location, the tests/thousand population, and the median population age of the countries where the studies were conducted. To assess statistical heterogeneity among the selected articles, the I2 statistic and the Cochran's Q test were used. Results Forty‐five studies involving R0 and 34 studies involving CFR were included. The pooled estimation of R0 was 2.69 (95% CI: 2.40, 2.98), and that of the CFR was 2.67 (2.25, 3.13). The CFR in different regions of the world varied significantly, from 2.49 (2.08, 2.94) in Asia to 3.40 (2.81, 4.04) in North America. We observed higher mean CFR values for the countries with lower tests (3.15 vs 2.16) and greater median population age (3.13 vs 2.27). However, R0 did not vary significantly in different regions of the world. Conclusions An R0 of 2.69 and a CFR of 2.67 indicate the severity of the COVID‐19. Although R0 and CFR may vary over time, space, and demographics, we recommend considering these figures in control and prevention measures.

In recent history, COVID-19 is one of the worst infectious disease outbreaks currently affecting humanity globally. Using real data on the COVID-19 outbreak from 22 January 2020 to 30 March 2020, we developed a mathematical model to investigate the impact of control measures in reducing the spread of the disease. Analyses of the model were carried out to determine the dynamics. The results of the analyses reveal that, using the data from China, implementing all possible control measures best reduced the rate of secondary infections. However, quarantine (isolation) of infectious individuals is shown to have the most dominant effect. This possibility emphasizes the need for extensive testing due to the possible prevalence of asymptomatic COVID-19 cases.

Coronavirus disease 2019 (COVID-19), which causes severe respiratory illness, has become a pandemic. The World Health Organization has declared it a public health crisis of international concern. We developed a susceptible, exposed, infected, recovered (SEIR) model for COVID-19 to show the importance of estimating the reproduction number (R0). This work is focused on predicting the COVID-19 outbreak in its early stage in India based on an estimation of R0. The developed model will help policymakers to take active measures prior to the further spread of COVID-19. Data on daily newly infected cases in India from March 2, 2020 to April 2, 2020 were to estimate R0 using the earlyR package. The maximum-likelihood approach was used to analyze the distribution of R0 values, and the bootstrap strategy was applied for resampling to identify the most likely R0 value. We estimated the median value of R0 to be 1.471 (95% confidence interval [CI], 1.351 to 1.592) and predicted that the new case count may reach 39,382 (95% CI, 34,300 to 47,351) in 30 days.

The basic reproduction number (R0), also called the basic reproduction ratio or rate or the basic reproductive rate, is an epidemiologic metric used to describe the contagiousness or transmissibility of infectious agents. R0 is affected by numerous biological, sociobehavioral, and environmental factors that govern pathogen transmission and, therefore, is usually estimated with various types of complex mathematical models, which make R0 easily misrepresented, misinterpreted, and misapplied. R0 is not a biological constant for a pathogen, a rate over time, or a measure of disease severity, and R0 cannot be modified through vaccination campaigns. R0 is rarely measured directly, and modeled R0 values are dependent on model structures and assumptions. Some R0 values reported in the scientific literature are likely obsolete. R0 must be estimated, reported, and applied with great caution because this basic metric is far from simple.

Objective: To investigate a measles outbreak that spread to Japan and Taiwan, China during March–May 2018, exploring the characteristics of the super-spreading event. Methods: A contact investigation of the index case and reconstruction of the epidemiological dynamics of measles transmission were conducted. Employing a mathematical model, the effective reproduction number was estimated for each generation of cases. Results and discussion: A single index case gave rise to a total of 38 secondary cases, 33 in Japan and five in Taiwan, China. Subsequent chains of transmission were observed in highly vaccinated populations in both Japan and Taiwan, China. The effective reproduction number of the second generation was >1 for both Japan and Taiwan, China. In Japan, the reproduction number was estimated to be

African swine fever (ASF) severely threatens the swine industry worldwide, given its spread and the absence of an available licensed vaccine, and has caused severe economic losses. Its persistence in wild boar (WB), longer than in domestic pig farms, and the knowledge gaps in ASF epidemiology hinder ASF virus (ASFV) eradication. Even in areas where disease is effectively controlled and ASFV is no longer detected, declaring eradication is difficult as seropositive WBs may still be detected. The aim of this work was to estimate the main ASF epidemiological parameters specific for the north of Sardinia, Italy. The estimated basic (R0) and effective (Re) reproduction numbers demonstrate that the ASF epidemic is declining and under control with an R0 of 1.139 (95% confidence interval (CI) = 1.123–1.153) and Re of 0.802 (95% CI = 0.612–0.992). In the last phases of an epidemic, these estimates are crucial tools for identifying the intensity of interventions required to definitively eradicate the disease. This approach is useful to understand if and when the detection of residual seropositive WB is no longer associated with any further ASFV circulation.

Background A Rohingya refugee camp in Cox’s Bazar, Bangladesh experienced a large-scale diphtheria epidemic in 2017. The background information of previously immune fraction among refugees cannot be explicitly estimated, and thus we conducted an uncertainty analysis of the basic reproduction number, R0. Methods A renewal process model was devised to estimate the R0 and ascertainment rate of cases, and loss of susceptible individuals was modeled as one minus the sum of initially immune fraction and the fraction naturally infected during the epidemic. To account for the uncertainty of initially immune fraction, we employed a Latin Hypercube sampling (LHS) method. Results R0 ranged from 4.7 to 14.8 with the median estimate at 7.2. R0 was positively correlated with ascertainment rates. Sensitivity analysis indicated that R0 would become smaller with greater variance of the generation time. Discussion Estimated R0 was broadly consistent with published estimate from endemic data, indicating that the vaccination coverage of 86% has to be satisfied to prevent the epidemic by means of mass vaccination. LHS was particularly useful in the setting of a refugee camp in which the background health status is poorly quantified.