Detection of multiple waves for COVID-19 and its optimal control through media awareness and vaccination: study based on some Indian states.

COVID-19 is a highly infectious disease, and in very recent times, it has shown a massive impact throughout the globe. Several countries faced the COVID-19 infection waves multiple times. These later waves are more aggressive than the first wave and drastically impact social and economic factors. We developed a mechanistic model with imperfect lockdown effect, reinfection, transmission variability between symptomatic & asymptomatic, and media awareness to focus on the early detection of multiple waves and their control measures. Using daily COVID-19 cases data from six states of India, we estimated several important model parameters. Moreover, we estimated the home quarantine, community, and basic reproduction numbers. We developed an algorithm to carry out global sensitivity analysis (Sobol) of the parameters that influence the number of COVID-19 waves ( W C ) and the average number of COVID-19 cases in a wave ( A W ). We have identified some critical controlling parameters that mainly influenced W C and A W . Our study also revealed the best COVID-19 control strategy/strategies among vaccination, media awareness, and their combination using an optimal cost-effective study. The detailed analysis suggests that the severity of asymptomatic transmission is around 10% to 29% of that of symptomatic transmission in all six locations. About 1% to 4% of the total population under lockdown may contribute to new COVID-19 infection in all six locations. Optimal cost-effective analysis based on interventions, namely only vaccination (VA), only media awareness (ME), and a combination of vaccination & media (VA+ME), are projected for the period March 14, 2020, to August 31, 2021, for all the six locations. We have found that a large percentage of the population (26% to 45%) must be vaccinated from February 13 to August 31, 2021, to avert an optimal number of COVID-19 cases in these six locations. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-022-07887-5.

The impact of a power law-induced memory effect on the SARS-CoV-2 transmission.

It is well established that COVID-19 incidence data follows some power law growth pattern. Therefore, it is natural to believe that the COVID-19 transmission process follows some power law. However, we found no existing model on COVID-19 with a power law effect only in the disease transmission process. Inevitably, it is not clear how this power law effect in disease transmission can influence multiple COVID-19 waves in a location. In this context, we developed a completely new COVID-19 model where a force of infection function in disease transmission follows some power law. Furthermore, different realistic epidemiological scenarios like imperfect social distancing among home-quarantined individuals, disease awareness, vaccination, treatment, and possible reinfection of the recovered population are also considered in the model. Applying some recent techniques, we showed that the proposed system converted to a COVID-19 model with fractional order disease transmission, where order of the fractional derivative ( α ) in the force of infection function represents the memory effect in disease transmission. We studied some mathematical properties of this newly formulated model and determined the basic reproduction number ( R 0 ). Furthermore, we estimated several epidemiological parameters of the newly developed fractional order model (including memory index α ) by fitting the model to the daily reported COVID-19 cases from Russia, South Africa, UK, and USA, respectively, for the time period March 01, 2020, till December 01, 2021. Variance-based Sobol's global sensitivity analysis technique is used to measure the effect of different important model parameters (including α ) on the number of COVID-19 waves in a location ( W C ). Our findings suggest that α along with the average transmission rate of the undetected (symptomatic and asymptomatic) cases in the community ( ß 1 ) are mainly influencing multiple COVID-19 waves in those four locations. Numerically, we identified the regions in the parameter space of α and ß 1 for which multiple COVID-19 waves are occurring in those four locations. Furthermore, our findings suggested that increasing memory effect in disease transmission ( α → 0) may decrease the possibility of multiple COVID-19 waves and as well as reduce the severity of disease transmission in those four locations. Based on all the results, we try to identify a few non-pharmaceutical control strategies that may reduce the risk of further SARS-CoV-2 waves in Russia, South Africa, UK, and USA, respectively.

Effective Lockdown and Role of Hospital-Based COVID-19 Transmission in Some Indian States: An Outbreak Risk Analysis.

Several reports in India indicate hospitals and quarantined centers are COVID-19 hotspots. To study the transmission occurring from the hospitals and as well as from the community, we developed a mechanistic model with a lockdown effect. Using daily COVID-19 cases data from six states and overall India, we estimated several important parameters of our model. Moreover, we provided an estimation of the effective (RT ), the basic (R0 ), the community (RC ), and the hospital (RH ) reproduction numbers. We forecast COVID-19 notified cases from May 3, 2020, till May 20, 2020, under five different lockdown scenarios in the seven locations. Our analysis suggests that 65% to 99% of the new COVID-19 cases are currently asymptomatic in those locations. Besides, about 1-16% of the total COVID-19 transmission are currently occurring from hospital-based contact and these percentage can increase up to 69% in some locations. Furthermore, the hospital-based transmission rate (ß2 ) has significant positive (0.65 to 0.8) and negative (-0.58 to -0.23) correlation with R0 and the effectiveness of lockdown, respectively. Therefore, a much larger COVID-19 outbreak may trigger from the hospital-based transmission. In most of the locations, model forecast from May 3, 2020, till May 20, 2020, indicates a two-times increase in cumulative cases in comparison to total observed cases up to April 29, 2020. Based on our results, we proposed a containment policy that may reduce the threat of a larger COVID-19 outbreak in the future.

Invasive dynamics for a predator-prey system with Allee effect in both populations and a special emphasis on predator mortality.

We considered a non-linear predator-prey model with an Allee effect on both populations on a two spatial dimension reaction-diffusion setup. Special importance to predator mortality was given as it may be often controlled through human-made harvesting processes. The local dynamics of the model was studied through boundedness, equilibrium, and stability analysis. An extensive numerical stability analysis was performed and found that bi-stability is not possible for the non-spatial model. By analyzing the spatial model, we found the condition for successful invasion and the persistence region of the species based on the predator Allee effect and its mortality parameter. Four different dynamics in this region of the parameter space are mainly explored. First, the Allee effect on both populations leads to various new types of species spread. Second, for a high value of per-capita growth rate, two completely new spreads (e.g., sun surface, colonial) have been found depending on the Allee effect parameter. Third, the Allee coefficient on the predator population leads to spatiotemporal chaos via a patchy spread for both linear and quadratic mortality rates. Finally, a more rigorous analysis is performed to study the chaotic nature of the system within the whole persistence domain. We have studied the possibility of chaos through temporal variation in different invasion regions. Furthermore, the chaotic fluctuation is studied through the sensitivity of initial conditions and by investigating the dominant Lyapunov exponent value.

Assessment of lockdown effect in some states and overall India: A predictive mathematical study on COVID-19 outbreak.

In the absence of neither an effective treatment or vaccine and with an incomplete understanding of the epidemiological cycle, Govt. has implemented a nationwide lockdown to reduce COVID-19 transmission in India. To study the effect of social distancing measure, we considered a new mathematical model on COVID-19 that incorporates lockdown effect. By validating our model to the data on notified cases from five different states and overall India, we estimated several epidemiologically important parameters as well as the basic reproduction number (R 0). Combining the mechanistic mathematical model with different statistical forecast models, we projected notified cases in the six locations for the period May 17, 2020, till May 31, 2020. A global sensitivity analysis is carried out to determine the correlation of two epidemiologically measurable parameters on the lockdown effect and also on R 0. Our result suggests that lockdown will be effective in those locations where a higher percentage of symptomatic infection exists in the population. Furthermore, a large scale COVID-19 mass testing is required to reduce community infection. Ensemble model forecast suggested a high rise in the COVID-19 notified cases in most of the locations in the coming days. Furthermore, the trend of the effective reproduction number (Rt ) during the projection period indicates if the lockdown measures are completely removed after May 17, 2020, a high spike in notified cases may be seen in those locations. Finally, combining our results, we provided an effective lockdown policy to reduce future COVID-19 transmission in India.

A realistic two-strain model for MERS-CoV infection uncovers the high risk for epidemic propagation.

Middle East Respiratory Syndrome Coronavirus (MERS-CoV) causes severe acute respiratory illness with a case fatality rate (CFR) of 35,5%. The highest number of MERS-CoV cases are from Saudi-Arabia, the major worldwide hotspot for this disease. In the absence of neither effective treatment nor a ready-to-use vaccine and with yet an incomplete understanding of its epidemiological cycle, prevention and containment measures can be derived from mathematical models of disease epidemiology. We constructed 2-strain models to predict past outbreaks in the interval 2012-2016 and derive key epidemiological information for Macca, Madina and Riyadh. We approached variability in infection through three different disease incidence functions capturing social behavior in response to an epidemic (e.g. Bilinear, BL; Non-monotone, NM; and Saturated, SAT models). The best model combination successfully anticipated the total number of MERS-CoV clinical cases for the 2015-2016 season and accurately predicted both the number of cases at the peak of seasonal incidence and the overall shape of the epidemic cycle. The evolution in the basic reproduction number (R0) warns that MERS-CoV may easily take an epidemic form. The best model correctly captures this feature, indicating a high epidemic risk (1≤R0≤2,5) in Riyadh and Macca and confirming the alleged co-circulation of more than one strain. Accurate predictions of the future MERS-CoV peak week, as well as the number of cases at the peak are now possible. These results indicate public health agencies should be aware that measures for strict containment are urgently needed before new epidemics take off in the region.

An open challenge to advance probabilistic forecasting for dengue epidemics.

A wide range of research has promised new tools for forecasting infectious disease dynamics, but little of that research is currently being applied in practice, because tools do not address key public health needs, do not produce probabilistic forecasts, have not been evaluated on external data, or do not provide sufficient forecast skill to be useful. We developed an open collaborative forecasting challenge to assess probabilistic forecasts for seasonal epidemics of dengue, a major global public health problem. Sixteen teams used a variety of methods and data to generate forecasts for 3 epidemiological targets (peak incidence, the week of the peak, and total incidence) over 8 dengue seasons in Iquitos, Peru and San Juan, Puerto Rico. Forecast skill was highly variable across teams and targets. While numerous forecasts showed high skill for midseason situational awareness, early season skill was low, and skill was generally lowest for high incidence seasons, those for which forecasts would be most valuable. A comparison of modeling approaches revealed that average forecast skill was lower for models including biologically meaningful data and mechanisms and that both multimodel and multiteam ensemble forecasts consistently outperformed individual model forecasts. Leveraging these insights, data, and the forecasting framework will be critical to improve forecast skill and the application of forecasts in real time for epidemic preparedness and response. Moreover, key components of this project-integration with public health needs, a common forecasting framework, shared and standardized data, and open participation-can help advance infectious disease forecasting beyond dengue.

Impact of adult mosquito control on dengue prevalence in a multi-patch setting: A case study in Kolkata (2014-2015).

Dengue is one of the deadliest mosquito-borne disease prevalent mainly in tropical and sub-tropical regions. Controlling the spread of this disease becomes a major concern to the public health authority. World Health Organization (WHO) adopted several mosquito control strategies to reduce the disease prevalence. In this work, a general multi-patch non-autonomous dengue model is formulated to capture the temporal and spatial transmission mechanism of the disease and the effectiveness of different adult mosquito control strategies in reducing dengue prevalence is evaluated. During the period (2014-2015) the dengue situation of Kolkata which is one of the most dengue affected city in India is considered in our study. Depending on geographical location, Kolkata is divided into five regions and our model is fitted to the monthly dengue cases of these five regions during the above-mentioned period. By considering control specific characteristics (e.g. efficacy, environment persistence) of the mosquito control strategies, we study the efficiency of three adult mosquito controls and their combined effect in reducing dengue prevalence. From our study, it is observed that control with higher environment persistence performs better in comparison to the controls having low environment persistence. It is also observed that, connectedness between the regions play a key role in the effectiveness of the control strategies.

Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.

In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R0). It is shown that if R0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic.

A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan.

In this manuscript, we propose and analyze a compartmental model of visceral leishmaniasis (VL). We model the human population with six compartments including asymptomatic, symptomatic and PKDL-infected, animal population as second host and sandfly population as the vector. Furthermore, the non-adult stage of the sandfly population is introduced in the system, which was not considered before in the literature. We show that the increase in the number of host of sandfly population generates a backward bifurcation. Thus, multiple hosts will cause disease persistence even if the basic reproduction number ([Formula: see text]) is below unity. We perform a sensitivity analysis of important model parameters with respect to some epidemiologically significant responses. We validate our model by calibrating it to weekly VL incidence data from South Sudan for the year 2013. We perform cost-effectiveness analysis on different interventions: treatment, non-adult control, adult control and their different layered combinations based on their implementation cost (in USD) and case reduction. We also use a global sensitivity analysis technique to understand the effect of important parameters of our model on the implementation cost of different controls. This cost-effectiveness study and cost-sensitivity analysis are relatively new in existing literature of this disease.

Estimating dengue type reproduction numbers for two provinces of Sri Lanka during the period 2013-14.

Dengue is an endemic disease in the southeast Asian country Sri Lanka. Two seasonal peaks of dengue incidence were observed every year since 2002 onwards. In this study, we formulate a 2-strain dengue model for analyzing the monthly seasonal dengue incidence data from 2 provinces of Sri Lanka during the period April 2013 to September 2014. The seasonality is incorporated in the model in terms of mosquito biting rate, which we assume to be time periodic. We estimated 2 primary reproduction numbers and the basic reproduction number in a periodic environment using dengue incidence data from the western and the central provinces of Sri Lanka. We also estimated different time-average type reproduction numbers from the model using the data from these 2 provinces. Using univariate sensitivity analysis, we measured the sensitivity of the time average reproduction number ([Formula: see text]) When we vary different parameters of the proposed dengue model, we find the transmission probability of human susceptibility to strain-I infection and the mosquito mortality rate parameters are the most sensitive parameters in dengue transmission in these 2 provinces.

A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector.

In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector.

An optimal cost effectiveness study on Zimbabwe cholera seasonal data from 2008-2011.

Incidence of cholera outbreak is a serious issue in underdeveloped and developing countries. In Zimbabwe, after the massive outbreak in 2008-09, cholera cases and deaths are reported every year from some provinces. Substantial number of reported cholera cases in some provinces during and after the epidemic in 2008-09 indicates a plausible presence of seasonality in cholera incidence in those regions. We formulate a compartmental mathematical model with periodic slow-fast transmission rate to study such recurrent occurrences and fitted the model to cumulative cholera cases and deaths for different provinces of Zimbabwe from the beginning of cholera outbreak in 2008-09 to June 2011. Daily and weekly reported cholera incidence data were collected from Zimbabwe epidemiological bulletin, Zimbabwe Daily cholera updates and Office for the Coordination of Humanitarian Affairs Zimbabwe (OCHA, Zimbabwe). For each province, the basic reproduction number ([Formula: see text]) in periodic environment is estimated. To the best of our knowledge, this is probably a pioneering attempt to estimate [Formula: see text] in periodic environment using real-life data set of cholera epidemic for Zimbabwe. Our estimates of [Formula: see text] agree with the previous estimate for some provinces but differ significantly for Bulawayo, Mashonaland West, Manicaland, Matabeleland South and Matabeleland North. Seasonal trend in cholera incidence is observed in Harare, Mashonaland West, Mashonaland East, Manicaland and Matabeleland South. Our result suggests that, slow transmission is a dominating factor for cholera transmission in most of these provinces. Our model projects [Formula: see text] cholera cases and [Formula: see text] cholera deaths during the end of the epidemic in 2008-09 to January 1, 2012. We also determine an optimal cost-effective control strategy among the four government undertaken interventions namely promoting hand-hygiene & clean water distribution, vaccination, treatment and sanitation for each province.