A Stochastic Model for Kala-azar Transmission Dynamics in Libo Kemkem, Ethiopia

The objective of this paper is to analyse and demonstrate the dynamics of Kala-azar infected group using stochastic model, particularly using simple SIR model with python script over time. The model is used under a closed population with N = 100, transmission rate coefficient β = 0.09, recovery rate γ = 0.03 and initial condition I(0) = 1. In the paper it is discussed how the Kala-azar infected group behaves through simple SIR model. The paper is completed with stochastic SIR model simulation result and shows stochasticity of the dynamics of Kala-azar infected population over time. Fig. 2 below depicts continuous fluctuations which tells us the disease evolves with stochastic nature and shows random process.Subject: Infectious Disease, Global Health, Health Informatics and Statistical and Computational Physics

A stochastic SIR model for analysis of testosterone suppression of CRH-stimulated cortisol in men

A stochastic SIR influenza vertical transmission model is examined in this paper where vaccination and an incidence rate that is not linear are considered. To determine whether testosterone regulates lower sintering HPA axis function in males, we used a stochastic SIR epidemic procedure with divergent influences on ACTH and cortisol. The suppressive effects on cortisol can be attributed to a peripheral (adrenal) locus. Following that, we came to the conclusion that experimental solutions have been discovered and the requisite statistical findings have been examined. Finally, we deduce that the given mathematical model and the results are relevant to medical research. In the future, this research can be further extended to simulate more results in the medical field.

Optimal Vaccination Campaigns Using Stochastic SIR Model and Multiobjective Impulsive Control

A multiobjective impulsive control scheme is proposed to give answers on how optimal vaccination campaigns should be implemented, regarding two conflicting targets: making the total number of infecteds small and the vaccination campaign as handy as possible. In this paper, a stochastic SIR model is used to better depict the characteristics of a disease in practical terms, where little influences may lead to sudden and unpredictable changes in the behavior of transmissions. This model is extended to analyze the effects of impulsive vaccinations in two phases: the transient regime control, taking into account the necessity to reduce the number of infected individuals to an acceptable level in a finite time, and the permanent regime control, that will act with fixed vaccinations to avoid another outbreak. A parallel version of NSGA-II is used as the multiobjective optimization machinery, considering both the probability of eradication and the vaccination campaign costs. The final result using the proposed framework nondominated policies that can guide for public managers to decide which is the best procedure to be taken depending on the present situation.

The nature of individual heterogeneity shape outbreak dynamics

It is now common-place that pathogen transmission during an outbreak can be more heterogeneous than what is commonly assumed, and that it can have major consequences on their dynamics. However, previous studies did not explore the impact of the different biological sources of heterogeneity while controlling for the resulting heterogeneity in the number of secondary cases. In this study, we explore the role of individual variation in infection duration and transmission rate on parasite emergence and spread in a population. We simulate outbreaks using a custom stochastic SIR model, with and without evolution of the parasite. We show that for a given mean, the variance in the number of secondary cases is the main driver of the outbreak probability, with or without evolution, while it does not play a role on the outbreak dynamic once it emerged. On the opposite, a smaller and more realistic variance in the infection duration causes a faster outbreak. It is therefore useful to take into consideration more realistic distributions when modelling infectious diseases outbreaks.

Stochastic extinction of epidemics: how long would it take for Sars-Cov-2 to die out without herd immunity?

Worldwide, we are currently in an unprecedented situation with regard to the SARS-Cov-2 epidemic, where countries are using isolation and lock-down measures to control the spread of infection. This is a scenario generally not much anticipated by previous theory, and in particular, there has been little attention paid to the question of extinction as a means to eradicate the virus; the prevailing view appears to be that this is unfeasible without a vaccine. We use a simple well-mixed stochastic SIR model as a basis for our considerations, and calculate a new result, using branching process theory, for the distribution of times to extinction. Surprisingly, the distribution is an extreme value distribution of the Gumbel type, and we show that the key parameter determining its mean and standard deviation is the expected rate of decline ρe = γ(1-Re) of infections, where γ is the rate of recovery from infection and Re is the usual effective reproductive number. The result also reveals a critical threshold number of infected I&#134 = 1/(1-Re), below which stochastic forces dominate and need be considered for accurate predictions. As this theory ignores migration between populations, we compare against a realistic spatial epidemic simulator and simple stochastic simulations of sub-divided populations with global migration, to find very comparable results to our simple predictions; in particular, we find global migration has the effect of a simple upwards rescaling of Re with the same Gumbel extinction time distribution we derive from our non-spatial model. Within the UK, assuming no migration, using recent estimates of I0≈37000 infected and Re= 0.9, this model predicts a mean extinction time of 616±90 days or approximately ~2 years, but could be as short as 123±15 days, or roughly 4 months for Re = 0.4; in practice, while there is prevalence of infections globally, it is likely that nations can only at best achieve quasi-extinction, a state of temporary extinction, when immigration of cases is rare. This highlights the importance of a global decline in infections, and here the theory predicts extinction in less than 200 days, if the reproductive number is restricted to Re < 0.5. Overall, these results highlight the extreme sensitivity of extinction times when Re approaches 1 and the necessity of reducing the effective reproductive number significantly (Re<≈0.5) for relatively rapid extinction of an epidemic or pandemic.

Modelling and Analysis of 2019-nCov Epidemic in India : A study on Attack & Recovery Rate, Basic & Effective Reproductive Number, Herd Immunity Threshold & Case Fatality Ratio of Coronavirus Covid-19 in India.

Mathematical modelling of any epidemic plays a crucial role in quantifying the impact of such pathogens. This paper focuses on building a Stochastic SIR Model with non-linear parameters (to account for the effect of lockdowns) to gain a broader cognition of the 2019 novel Coronavirus pathogen (2019-nCov), widely known as Covid-19, in India. Such models help in gauging the virulence and fecundity of pathogens. Based on early transmission dynamics the basic reproductive number (R0) is computed to be 1.605. Whereas, effective reproductive number (Rt) is computed to be 4.880 as on 19 March, 2.756 as on 19 April, and 1.995 as on 19 May. Furthermore, the proportion of population that needs to be immunized (through inoculation, recovery, or death) to halt the infection spread is estimated to be 37.69%, ergo, the Herd Immunity Threshold is estimated to be 51.36 crores recoveries, if the Rt remains below 2. Rt is expected to fall below 2, and the Case Fatality Ratio (CFR) to fall to 2.14%, circa early-September (assuming minimal or no medical breakthroughs). The formulated model also provides inferential evidence manifesting the extent to which lockdowns contained the spread of the virus.