Understanding the Role of Environmental Transmission on COVID-19 Herd Immunity and Invasion Potential.

COVID-19 is caused by the SARS-CoV-2 virus, which is mainly transmitted directly between humans. However, it is observed that this disease can also be transmitted through an indirect route via environmental fomites. The development of appropriate and effective vaccines has allowed us to target and anticipate herd immunity. Understanding of the transmission dynamics and the persistence of the virus on environmental fomites and their resistive role on indirect transmission of the virus is an important scientific and public health challenge because it is essential to consider all possible transmission routes and route specific transmission strength to accurately quantify the herd immunity threshold. In this paper, we present a mathematical model that considers both direct and indirect transmission modes. Our analysis focuses on establishing the disease invasion threshold, investigating its sensitivity to both transmission routes and isolate route-specific transmission rate. Using the tau-leap algorithm, we perform a stochastic model simulation to address the invasion potential of both transmission routes. Our analysis shows that direct transmission has a higher invasion potential than that of the indirect transmission. As a proof of this concept, we fitted our model with early epidemic data from several countries to uniquely estimate the reproduction numbers associated with direct and indirect transmission upon confirming the identifiability of the parameters. As the indirect transmission possess lower invasion potential than direct transmission, proper estimation and necessary steps toward mitigating it would help reduce vaccination requirement.

Optimal control problems of mosquito-borne disease subject to changes in feeding behavior of Aedes mosquitoes.

Dengue viruses (DENV) are transmitted to humans by the bite of Aedes mosquitoes. It is known that dengue virus infection in Aedes aegypti female mosquitoes makes a change in the feeding behavior of the infected mosquitoes. In this study, using the forces of infection, we incorporated the effect of changes in the feeding behavior of mosquitoes into the standard vector-borne SIR-SI model. It has been proved that both a single-strain model and a two-strain model exhibit forward bifurcations. Moreover, optimal implementations of control with specific prevention measures for dengue transmission are analyzed. As a result we found that more implementation of controls on the secondary infection of humans should be considered for the behavioral changes in feeding of the infected mosquitoes.

Optimal implementation of intervention strategies for elderly people with ludomania.

OBJECTIVES: Now-a-days gambling is growing especially fast among older adults. To control the gratuitous growth of gambling, well-analyzed scientific strategies are necessary. We tried to analyze the adequacy of the health of society mathematically through immediate treatment of patients with early prevention. METHODS: The model from Lee and Do was modified and control parameters were introduced. Pontryagin's Maximum Principle was used to obtain an optimal control strategy. RESULTS: Optimal control can be achieved through simultaneous use of the control parameters, though it varies from society to society. The control corresponding to prevention needed to be implemented in full almost all the time for all types of societies. In the case of the other two controls, the scenario was greatly affected depending on the types of societies. CONCLUSION: Prevention and treatment for elderly people with ludomania are the main intervention strategies. We found that optimal timely implementation of the intervention strategies was more effective. The optimal control strategy varied with the initial number of gamblers. However, three intervention strategies were considered, among which, preventing people from engaging in all types of gambling proved to be the most crucial.

Optimal Implementation of Intervention to Control the Self-harm Epidemic.

OBJECTIVES: Deliberate self-harm (DSH) of a young person has been a matter of growing concern to parents and policymakers. Prevention and early eradication are the main interventional techniques among which prevention through reducing peer pressure has a major role in reducing the DSH epidemic. Our aim is to develop an optimal control strategy for minimizing the DSH epidemic and to assess the efficacy of the controls. METHODS: We considered a deterministic compartmental model of the DSH epidemic and two interventional techniques as the control measures. Pontryagin's Maximum Principle was used to mathematically derive the optimal controls. We also simulated the model using the forward-backward sweep method. RESULTS: Simulation results showed that the controls needed to be used simultaneously to reduce DSH successfully. An optimal control strategy should be adopted, depending on implementation costs for the controls. CONCLUSION: The long-term success of the optimum control depends on the implementation cost. If the cost is very high, the control could be used for a short term, even though it fails in the long run. The control strategy, most importantly, should be implemented as early as possible to attack a comparatively fewer number of addicted individuals.

Optimal Control Strategy of Plasmodium vivax Malaria Transmission in Korea.

OBJECTIVE: To investigate the optimal control strategy for Plasmodium vivax malaria transmission in Korea. METHODS: A Plasmodium vivax malaria transmission model with optimal control terms using a deterministic system of differential equations is presented, and analyzed mathematically and numerically. RESULTS: If the cost of reducing the reproduction rate of the mosquito population is more than that of prevention measures to minimize mosquito-human contacts, the control of mosquito-human contacts needs to be taken for a longer time, comparing the other situations. More knowledge about the actual effectiveness and costs of control intervention measures would give more realistic control strategies. CONCLUSION: Mathematical model and numerical simulations suggest that the use of mosquito-reduction strategies is more effective than personal protection in some cases but not always.

A model for the transmission dynamics of Orientia tsutsugamushi among its natural reservoirs.

The bacteria Orientia tsutsugamushi is the causative agent of scrub typhus, a prevalent disease in Asian countries that can affect humans and which shows an alarming increase of cases during the last years, especially in rural areas. Unfortunately, there is no vaccine for scrub typhus, and antibiotic treatments successfully used in the past appear to be inefficient to treat some strains of O. tsutsugamushi. We introduce a mathematical model that approximates the dynamics of the bacteria among its natural reservoirs. After computing the basic reproductive number from the proposed model, we explore its sensitivity to the parameter values that may be affected by application of control measures. This theoretical model may be of interest to pest managers as well as health authorities interested in gaining insight into the public management of the disease, through a better understanding of its qualitative dynamics.