arXiv subjects

Tridip Sardar

Publications and source records attributed to Tridip Sardar.

3 recordsLinked to original sources

arXiv2024

Global stability and optimal control in a single-strain dengue model with fractional-order transmission and recovery process

The current manuscript introduce a single-strain dengue model developed from stochastic processes incorporating fractional order transmission and recovery. The fractional derivative has been introduced within the context of transmission and recovery process, displaying characteristics similar to tempered fractional ($TF$) derivatives. It has been established that under certain condition, a function's $TF$ derivatives are proportional to the function itself. Applying the following observation, we examined stability of several steady-state solutions, such as disease-free and endemic states, in light of this newly formulated model, using the reproduction number (R_0). In addition, the precise range of epidemiological parameters for the fractional order model was determined by calibrating weekly registered dengue incidence in the San Juan municipality of Puerto Rico, from April 9, 2010, to April 2, 2011. We performed a global sensitivity analysis method to measure the influence of key model parameters (along with the fractional-order coefficient) on total dengue cases and the basic reproduction number (R_0) using a Monte Carlo-based partial rank correlation coefficient (PRCC). Moreover, we formulated a fractional-order model with fractional control to asses the effectiveness of different interventions, such as reduction the recruitment rate of mosquito breeding, controlling adult vector, and providing individual protection. Also, we established the existence of a solution for the fractional-order optimal control problem. Finally, the numerical experiment illustrates that, policymakers should place importance on the fractional order transmission and recovery parameters that capture the underline mechanisms of disease along with reducing the spread of dengue cases, carried out through the implementation of two vector controls.

math.DS↗

arXiv2020

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 ($R_{t}$) 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.

q-bio.PE↗

arXiv2020

Effective lockdown and role of hospital-based COVID-19 transmission in some Indian states: An outbreak risk analysis

There are several reports in India that indicate hospitals and quarantined centers are COVID-19 hotspots. In the absence of efficient contact tracing tools, Govt. and the policymakers may not be paying attention to the risk of hospital-based transmission. To explore more on this important route and its possible impact on lockdown effect, we developed a mechanistic model with hospital-based transmission. Using daily notified COVID-19 cases from six states (Maharashtra, Delhi, Madhya Pradesh, Rajasthan, Gujarat, and Uttar Pradesh) and overall India, we estimated several important parameters of the model. Moreover, we provided an estimation of the basic ($R_{0}$), the community ($R_{C}$), and the hospital ($R_{H}$) reproduction numbers for those seven locations. To obtain a reliable forecast of future COVID-19 cases, a BMA post-processing technique is used to ensemble the mechanistic model with a hybrid statistical model. Using the ensemble model, we forecast COVID-19 notified cases (daily and cumulative) from May 3, 2020, till May 20, 2020, under five different lockdown scenarios in the mentioned locations. Our analysis of the mechanistic model suggests that most of the new COVID-19 cases are currently undetected in the mentioned seven locations. Furthermore, a global sensitivity analysis of four epidemiologically measurable \& controllable parameters on $R_{0}$ and as well on the lockdown effect, indicate that if appropriate preventive measures are not taken immediately, a much larger COVID-19 outbreak may trigger from hospitals and quarantined centers. In most of the locations, our ensemble model forecast indicates a substantial percentage of increase in the COVID-19 notified cases in the coming weeks in India. Based on our results, we proposed a containment policy that may reduce the threat of a larger COVID-19 outbreak in the coming days.

q-bio.PE↗