Model-Based Estimation of Expected Time to Cholera Extinction in Lusaka, Zambia.

The developing world has been facing a significant health issue due to cholera as an endemic communicable disease. Lusaka was Zambia's worst affected province, with 5414 reported cases of cholera during the outbreak from late October 2017 to May 12, 2018. To explore the epidemiological characteristics associated with the outbreak, we fitted weekly reported cholera cases with a compartmental disease model that incorporates two transmission routes, namely environment-to-human and human-to-human.

A noble extended stochastic logistic model for cell proliferation with density-dependent parameters.

Cell proliferation often experiences a density-dependent intrinsic proliferation rate (IPR) and negative feedback from growth-inhibiting molecules in culture media. The lack of flexible models with explanatory parameters fails to capture such a proliferation mechanism. We propose an extended logistic growth law with the density-dependent IPR and additional negative feedback.

An extended stochastic Allee model with harvesting and the risk of extinction of the herring population.

Overexploitation of commercially beneficial fish is a serious ecological problem around the world. The growth profiles of most of the species are likely to follow density regulated theta-logistic model irrespective of any taxonomy group [Sibly et al., Science, 2005].

Chance of extinction of populations in food chain model under demographic stochasticity.

The extinction of different species from the earth is increasing at an alarming rate. So, assessment of probability of extinction of different important species in our ecosystem could help us to take proper conservation policy for those population whose chance of extinction is high. In this paper a method is developed to find the probability of extinction of populations in a general n-trophic food chain model under demographic stochasticity.

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.