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The COVID-19 pandemic, caused by SARS-CoV-2, disproportionately affected certain segments of society, particularly the elderly population (which suffered the brunt of the burden of the pandemic in terms of severity of the disease, hospitalization, and death). This study presents a generalized multigroup model, with m heterogeneous sub-populations, to assess the population-level impact of age heterogeneity and vaccination on the transmission dynamics and control of the SARS-CoV-2 pandemic in the United States. Rigorous analysis of the model for the homogeneous case (i.e., the model with m = 1) reveal that its disease-free equilibrium is globally-asymptotically stable for two special cases (with perfect vaccine efficacy or negligible disease-induced mortality) whenever the associated reproduction number is less than one. The model has a unique and globally-asymptotically stable endemic equilibrium, for special a case, when the associated reproduction threshold exceeds one. The homogeneous model was fitted using the observed cumulative mortality data for the United States during three distinct waves (Waves A (October 17, 2020 to April 5, 2021), B (July 9, 2021 to November 7, 2021) and C (January 1, 2022 to May 7, 2022)) chosen to align with time periods when the Alpha, Delta and Omicron were, respectively, the predominant variants in the United States. The calibrated model was used to derive a theoretical expression for achieving vaccine-derived herd immunity (needed to eliminate the disease in the United States). It was shown that, using the one-group homogeneous model, vaccine-derived herd immunity is not attainable during Wave C of the pandemic in the United States, regardless of the coverage level of the fully-vaccinated individuals. Global sensitivity analysis was carried out to determine the parameters of the model that have the most influence on the disease dynamics and burden. These analyses reveal that control and mitigation strategies that may be very effective during one wave may not be so very effective during the other wave or waves. However, strategies that target asymptomatic and pre-symptomatic infectious individuals are shown to be consistently effective across all waves. To study the impact of the disproportionate effect of COVID-19 on the elderly population, we considered the heterogeneous model for the case where the total population is subdivided into the sub-populations of individuals under 65 years of age and those that are 65 and older. The resulting two-group heterogeneous model, which was also fitted using the cumulative mortality data for wave C, was also rigorously analysed. Unlike for the case of the one-group model, it was shown, for the two-group model, that vaccine-derived herd immunity can indeed be achieved during Wave C of the pandemic if at least 61% of the populace is fully vaccinated. Thus, this study shows that adding age heterogeneity into a SARS-CoV-2 vaccination model with homogeneous mixing significantly reduces the level of vaccination coverage needed to achieve vaccine-derived herd immunity (specifically, for the heterogeneous model, herd-immunity can be attained during Wave C if a moderate proportion of susceptible individuals are fully vaccinated). The consequence of this result is that vaccination models for SARS-CoV-2 that do not explicitly account for age heterogeneity may be overestimating the level of vaccine-derived herd immunity threshold needed to eliminate the SARS-CoV-2 pandemic.

A new mathematical model for the transmission dynamics and control of the Middle Eastern respiratory syndrome (MERS), a respiratory virus caused by MERS-CoV coronavirus (and primarily spread to humans by dromedary camels) that first emerged out of the Kingdom of Saudi Arabia (KSA) in 2012, was designed and used to study the transmission dynamics of the disease in a human-camel population within the KSA. Rigorous analysis of the model, which was fitted and cross-validated using the observed MERS-CoV data for the KSA, showed that its disease-free equilibrium was locally asymptotically stable whenever its reproduction number (denoted by $ {\mathbb R}_{0M} $) was less than unity. Using the fixed and estimated parameters of the model, the value of $ {\mathbb R}_{0M} $ for the KSA was estimated to be 0.84, suggesting that the prospects for MERS-CoV elimination are highly promising. The model was extended to allow for the assessment of public health intervention strategies, notably the potential use of vaccines for both humans and camels and the use of face masks by humans in public or when in close proximity with camels. Simulations of the extended model showed that the use of the face mask by humans who come in close proximity with camels, as a sole public health intervention strategy, significantly reduced human-to-camel and camel-to-human transmission of the disease, and this reduction depends on the efficacy and coverage of the mask type used in the community. For instance, if surgical masks are prioritized, the disease can be eliminated in both the human and camel population if at least 45% of individuals who have close contact with camels wear them consistently. The simulations further showed that while vaccinating humans as a sole intervention strategy only had marginal impact in reducing the disease burden in the human population, an intervention strategy based on vaccinating camels only resulted in a significant reduction in the disease burden in camels (and, consequently, in humans as well). Thus, this study suggests that attention should be focused on effectively combating the disease in the camel population, rather than in the human population. Furthermore, the extended model was used to simulate a hybrid strategy, which combined vaccination of both humans and camels as well as the use of face masks by humans. This simulation showed a marked reduction of the disease burden in both humans and camels, with an increasing effectiveness level of this intervention, in comparison to the baseline scenario or any of the aforementioned sole vaccination scenarios. In summary, this study showed that the prospect of the elimination of MERS-CoV-2 in the Kingdom of Saudi Arabia is promising using pharmaceutical (vaccination) and nonpharmaceutical (mask) intervention strategies, implemented in isolation or (preferably) in combination, that are focused on reducing the disease burden in the camel population.

Although much progress has been made in reducing the public health burden of the human immunodeficiency virus (HIV), which causes acquired immunodeficiency syndrome (AIDS), since its emergence in the 1980s (largely due to the large-scale use and availability of potent antiviral therapy, improved diagnostic and intervention and mitigation measures), HIV remains an important public health challenge globally, including in the United States. This study is based on the use of mathematical modeling approaches to assess the population-level impact of pre-exposure prophylaxis (PrEP), voluntary testing (to detect undetected HIV-infected individuals), and changes in human behavior (with respect to risk structure), on the spread and control of HIV/AIDS in an MSM (men-who-have sex-with-men) population. Specifically, a novel two-group mathematical model, which stratifies the total MSM population based on risk (low or high) of acquisition of HIV infection, is formulated. The model undergoes a PrEP-induced backward bifurcation when the control reproduction number of the model is less than one if the efficacy of PrEP to prevent a high-risk susceptible MSM individual from acquiring HIV infection is not perfect (the consequence of which is that, while necessary, having the reproduction number of the model less than one is no longer sufficient for the elimination of the disease in the MSM population). For the case where the efficacy of PrEP is perfect, this study shows that the disease-free equilibrium of the two-group model is globally-asymptotically stable when the associated control reproduction number of the model is less than one. Global sensitivity analysis was carried out to identify the main parameters of the model that have the highest influence on the value of the control reproduction number of the model (thereby, having the highest influence on the disease burden in the MSM population). Numerical simulations of the model, using a plausible range of parameter values, show that if half of the MSM population considered adhere strictly to the specified PrEP regimen (while other interventions are maintained at their baseline values), a reduction of about 22% of the new yearly HIV cases recorded at the peak of the disease could be averted (compared to the worst-case scenario where PrEP-based intervention is not implemented in the MSM population). The yearly reduction at the peak increases to about 50% if the PrEP coverage in the MSM population increases to 80%. This study showed, based on the parameter values used in the simulations, that the prospects of elimination of HIV/AIDS in the MSM community are promising if high-risk susceptible individuals are no more than 15% more likely to acquire HIV infection, in comparison to their low-risk counterparts. Furthermore, these prospects are significantly improved if undetected HIV-infected individuals are detected within an optimal period of time.

Three safe and effective vaccines against SARS-CoV-2 have played a major role in combating COVID-19 in the United States. However, the effectiveness of these vaccines and vaccination programs has been challenged by the emergence of new SARS-CoV-2 variants of concern. A new mathematical model is formulated to assess the impact of waning and boosting of immunity against the Omicron variant in the United States. To account for gradual waning of vaccine-derived immunity, we considered three vaccination classes that represent high, moderate and low levels of immunity. We showed that the disease-free equilibrium of the model is globally-asymptotically, for two special cases, if the associated reproduction number is less than unity. Simulations of the model showed that vaccine-derived herd immunity can be achieved in the United States via a vaccination-boosting strategy which entails fully vaccinating at least 59% of the susceptible populace followed by the boosting of about 72% of the fully-vaccinated individuals whose vaccine-derived immunity has waned to moderate or low level. In the absence of boosting, waning of immunity only causes a marginal increase in the average number of new cases at the peak of the pandemic, while boosting at baseline could result in a dramatic reduction in the average number of new daily cases at the peak. Specifically, for the fast immunity waning scenario (where both vaccine-derived and natural immunity are assumed to wane within three months), boosting vaccine-derived immunity at baseline reduces the average number of daily cases at the peak by about 90% (in comparison to the corresponding scenario without boosting of the vaccine-derived immunity), whereas boosting of natural immunity (at baseline) only reduced the corresponding peak daily cases (in comparison to the corresponding scenario without boosting of natural immunity) by approximately 62%. Furthermore, boosting of vaccine-derived immunity is more beneficial (in reducing the burden of the pandemic) than boosting of natural immunity. Finally, boosting vaccine-derived immunity increased the prospects of altering the trajectory of COVID-19 from persistence to possible elimination.

This study presents a genetic-ecology modeling framework for assessing the combined impacts of insecticide resistance, temperature variability, and insecticide-based interventions on the population abundance and control of malaria mosquitoes by genotype. Rigorous analyses of the model we developed reveal that the boundary equilibrium with only mosquitoes of homozygous sensitive (resistant) genotype is locally-asymptotically stable whenever a certain ecological threshold, denoted by R0SS(R0RR), is less than one. Furthermore, genotype i drives genotype j to extinction whenever R0j>1 and R0i1), the two boundary equilibria lose their stability, and a coexistence equilibrium (where all three mosquito genotypes coexist) becomes locally-asymptotically stable. Global sensitivity analysis shows that the key parameters that greatly influence the dynamics and population abundance of resistant mosquitoes include the proportion of new adult mosquitoes that are females, the insecticide-induced mortality rate of adult female mosquitoes, the coverage level and efficacy of adulticides used in the community, the oviposition rates for eggs of heterozygous and homozygous resistant genotypes, and the modification parameter accounting for the reduction in insecticide-induced mortality due to resistance. Numerical simulations show that the adult mosquito population increases with increasing temperature until a peak is reached at 31 °C, and declines thereafter. Simulating the model for moderate and high adulticide coverage, together with varying fitness costs of resistance, shows a switch in the dominant genotype at equilibrium as temperature is varied. In other words, this study shows that, for certain combinations of adulticide coverage and fitness costs of insecticide resistance, increases in temperature could result in effective management of resistance (by causing the switch from a stable resistant-only boundary equilibrium (at 18 °C) to a stable sensitive-only boundary equilibrium (at 25 °C)). Finally, this study shows that, for moderate fitness costs of resistance, density-dependent larval mortality suppresses the total population of adult mosquitoes with the resistant allele for all temperature values in the range [18 °C–36 °C].

The novel coronavirus (COVID-19) pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world. It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic. Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic. This study presents a primer for formulating, analysing and simulating mathematical models for understanding the dynamics of COVID-19. Specifically, we introduce simple compartmental, Kermack-McKendrick-type epidemic models with homogeneously- and heterogeneously-mixed populations, an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine. We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model. A brief overview of other kinds of models that have been used to study the dynamics of COVID-19, such as agent-based, network and statistical models, is also presented. Possible extensions of the basic model, as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics, are suggested.

Multiple effective vaccines are currently being deployed to combat the COVID-19 pandemic, and are viewed as the major factor in marked reductions of disease burden in regions with moderate to high vaccination coverage. The effectiveness of COVID-19 vaccination programs is, however, significantly threatened by the emergence of new SARS-COV-2 variants that, in addition to being more transmissible than the wild-type (original) strain, may at least partially evade existing vaccines. A two-strain (one wild-type, one variant) and two-group (vaccinated or otherwise) mechanistic mathematical model is designed and used to assess the impact of the vaccine-induced cross-protective efficacy on the spread the COVID-19 pandemic in the United States. Rigorous analysis of the model shows that, in the absence of any co-circulating SARS-CoV-2 variant, the vaccine-derived herd immunity threshold needed to eliminate the wild-type strain can be achieved if 59% of the US population is fully-vaccinated with either the Pfizer or Moderna vaccine. This threshold increases to 76% if the wild-type strain is co-circulating with the Alpha variant (a SARS-CoV-2 variant that is 56% more transmissible than the wild-type strain). If the wild-type strain is co-circulating with the Delta variant (which is estimated to be 100% more transmissible than the wild-type strain), up to 82% of the US population needs to be vaccinated with either of the aforementioned vaccines to achieve the vaccine-derived herd immunity. Global sensitivity analysis of the model reveal the following four parameters as the most influential in driving the value of the reproduction number of the variant strain (hence, COVID-19 dynamics) in the US: (a) the infectiousness of the co-circulating SARS-CoV-2 variant, (b) the proportion of individuals fully vaccinated (using Pfizer or Moderna vaccine) against the wild-type strain, (c) the cross-protective efficacy the vaccines offer against the variant strain and (d) the modification parameter accounting for the reduced infectiousness of fully-vaccinated individuals experiencing breakthrough infection. Specifically, numerical simulations of the model show that future waves or surges of the COVID-19 pandemic can be prevented in the US if the two vaccines offer moderate level of cross-protection against the variant (at least 67%). This study further suggests that a new SARS-CoV-2 variant can cause a significant disease surge in the US if (i) the vaccine coverage against the wild-type strain is low (roughly

India has been the latest global epicenter for COVID-19, a novel coronavirus disease that emerged in China in late 2019. We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbor, Pakistan. The base model was rigorously analyzed and parameterized using cumulative COVID-19 mortality data from each of the two countries. The model was used to assess the population-level impact of the control and mitigation strategies implemented in the two countries (notably non-pharmaceutical interventions). Numerical simulations of the basic model indicate that, based on the current baseline levels of the control and mitigation strategies implemented, the pandemic trajectory in India is on a downward trend. This downward trend will be reversed, and India will be recording mild outbreaks, if the control and mitigation strategies are relaxed from their current levels. By early September 2021, our simulations suggest that India could record up to 460,000 cumulative deaths under baseline levels of the implemented control strategies, while Pakistan (where the pandemic is comparatively milder) could see over 24,000 cumulative deaths at current mitigation levels. The basic model was extended to assess the impact of back-and-forth mobility between the two countries. Simulations of the resulting metapopulation model show that the burden of the COVID-19 pandemic in Pakistan increases with increasing values of the average time residents of India spend in Pakistan, with daily mortality in Pakistan peaking in mid-August to mid-September of 2021. Under the respective baseline control scenarios, our simulations show that the back-and-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in India and Pakistan to November 2022 and July 2022, respectively.

A mathematical model is designed and used to study the transmission dynamics and control of COVID-19 in Nigeria. The model, which was rigorously analysed and parametrized using COVID-19 data published by the Nigeria Centre for Disease Control (NCDC), was used to assess the community-wide impact of various control and mitigation strategies in some jurisdictions within Nigeria (notably the states of Kano and Lagos, and the Federal Capital Territory, Abuja). Numerical simulations of the model showed that COVID-19 can be effectively controlled in Nigeria using moderate levels of social-distancing strategy in the jurisdictions and in the entire nation. Although the use of face masks in public can significantly reduce COVID-19 in Nigeria, its use, as a sole intervention strategy, may fail to lead to a substantial reduction in disease burden. Such substantial reduction is feasible in the jurisdictions (and the entire Nigerian nation) if the public face mask use strategy is complemented with a social-distancing strategy. The community lockdown measures implemented in Nigeria on March 30, 2020 need to be maintained for at least three to four months to lead to the effective containment of COVID-19 outbreaks in the country. Relaxing, or fully lifting, the lockdown measures sooner, in an effort to re-open the economy or the country, may trigger a deadly second wave of the pandemic.

Face mask use by the general public for limiting the spread of the COVID-19 pandemic is controversial, though increasingly recommended, and the potential of this intervention is not well understood. We develop a compartmental model for assessing the community-wide impact of mask use by the general, asymptomatic public, a portion of which may be asymptomatically infectious. Model simulations, using data relevant to COVID-19 dynamics in the US states of New York and Washington, suggest that broad adoption of even relatively ineffective face masks may meaningfully reduce community transmission of COVID-19 and decrease peak hospitalizations and deaths. Moreover, mask use decreases the effective transmission rate in nearly linear proportion to the product of mask effectiveness (as a fraction of potentially infectious contacts blocked) and coverage rate (as a fraction of the general population), while the impact on epidemiologic outcomes (death, hospitalizations) is highly nonlinear, indicating masks could synergize with other non-pharmaceutical measures. Notably, masks are found to be useful with respect to both preventing illness in healthy persons and preventing asymptomatic transmission. Hypothetical mask adoption scenarios, for Washington and New York state, suggest that immediate near universal (80%) adoption of moderately (50%) effective masks could prevent on the order of 17–45% of projected deaths over two months in New York, while decreasing the peak daily death rate by 34–58%, absent other changes in epidemic dynamics. Even very weak masks (20% effective) can still be useful if the underlying transmission rate is relatively low or decreasing: In Washington, where baseline transmission is much less intense, 80% adoption of such masks could reduce mortality by 24–65% (and peak deaths 15–69%), compared to 2–9% mortality reduction in New York (peak death reduction 9–18%). Our results suggest use of face masks by the general public is potentially of high value in curtailing community transmission and the burden of the pandemic. The community-wide benefits are likely to be greatest when face masks are used in conjunction with other non-pharmaceutical practices (such as social-distancing), and when adoption is nearly universal (nation-wide) and compliance is high.

The novel coronavirus (COVID-19) that emerged from Wuhan city of China in late December 2019 continue to pose devastating public health and economic challenges across the world. Although the community-wide implementation of basic non-pharmaceutical intervention measures, such as social distancing, quarantine of suspected COVID-19 cases, isolation of confirmed cases, use of face masks in public, contact tracing and testing, have been quite effective in curtailing and mitigating the burden of the pandemic, it is universally believed that the use of a vaccine may be necessary to effectively curtail and eliminating COVID-19 in human populations. This study is based on the use of a mathematical model for assessing the impact of a hypothetical imperfect anti-COVID-19 vaccine on the control of COVID-19 in the United States. An analytical expression for the minimum percentage of unvaccinated susceptible individuals needed to be vaccinated in order to achieve vaccine-induced community herd immunity is derived. The epidemiological consequence of the herd immunity threshold is that the disease can be effectively controlled or eliminated if the minimum herd immunity threshold is achieved in the community. Simulations of the model, using baseline parameter values obtained from fitting the model with COVID-19 mortality data for the U.S., show that, for an anti-COVID-19 vaccine with an assumed protective efficacy of 80%, at least 82% of the susceptible US population need to be vaccinated to achieve the herd immunity threshold. The prospect of COVID-19 elimination in the US, using the hypothetical vaccine, is greatly enhanced if the vaccination program is combined with other interventions, such as face mask usage and/or social distancing. Such combination of strategies significantly reduces the level of the vaccine-induced herd immunity threshold needed to eliminate the pandemic in the US. For instance, the herd immunity threshold decreases to 72% if half of the US population regularly wears face masks in public (the threshold decreases to 46% if everyone wears a face mask).

Dynamic models are used to assess the impact of three types of face masks (cloth masks, surgical/procedure masks and respirators) in controlling the COVID-19 pandemic in the USA. We showed that the pandemic would have failed to establish in the USA if a nationwide mask mandate, based on using respirators with moderately high compliance, had been implemented during the first two months of the pandemic. The other mask types would fail to prevent the pandemic from becoming established. When mask usage compliance is low to moderate, respirators are far more effective in reducing disease burden. Using data from the third wave, we showed that the epidemic could be eliminated in the USA if at least 40% of the population consistently wore respirators in public. Surgical masks can also lead to elimination, but requires compliance of at least 55%. Daily COVID-19 mortality could be eliminated in the USA by June or July 2021 if 95% of the population opted for either respirators or surgical masks from the beginning of the third wave. We showed that the prospect of effective control or elimination of the pandemic using mask-based strategy is greatly enhanced if combined with other non-pharmaceutical interventions (NPIs) that significantly reduce the baseline community transmission. By slightly modifying the model to include the effect of a vaccine against COVID-19 and waning vaccine-derived and natural immunity, this study shows that the waning of such immunity could trigger multiple new waves of the pandemic in the USA. The number, severity and duration of the projected waves depend on the quality of mask type used and the level of increase in the baseline levels of other NPIs used in the community during the onset of the third wave of the pandemic in the USA. Specifically, no severe fourth or subsequent wave of the pandemic will be recorded in the USA if surgical masks or respirators are used, particularly if the mask use strategy is combined with an increase in the baseline levels of other NPIs. This study further emphasizes the role of human behaviour towards masking on COVID-19 burden, and highlights the urgent need to maintain a healthy stockpile of highly effective respiratory protection, particularly respirators, to be made available to the general public in times of future outbreaks or pandemics of respiratory diseases that inflict severe public health and socio-economic burden on the population.

A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that inflicted unprecedented public health and economic burden in all nooks and corners of the world. Although the control of COVID-19 largely focused on the use of basic public health measures (primarily based on using non-pharmaceutical interventions, such as quarantine, isolation, social-distancing, face mask usage, and community lockdowns) initially, three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc., and Pfizer Inc.), were approved for use in humans in December 2020. We present a new mathematical model for assessing the population-level impact of these vaccines on curtailing the burden of COVID-19. The model stratifies the total population into two subgroups, based on whether or not they habitually wear face mask in public. The resulting multigroup model, which takes the form of a deterministic system of nonlinear differential equations, is fitted and parameterized using COVID-19 cumulative mortality data for the third wave of the COVID-19 pandemic in the United States. Conditions for the asymptotic stability of the associated disease-free equilibrium, as well as an expression for the vaccine-derived herd immunity threshold, are rigorously derived. Numerical simulations of the model show that the size of the initial proportion of individuals in the mask-wearing group, together with positive change in behavior from the non-mask wearing group (as well as those in the mask-wearing group, who do not abandon their mask-wearing habit) play a crucial role in effectively curtailing the COVID-19 pandemic in the United States. This study further shows that the prospect of achieving vaccine-derived herd immunity (required for COVID-19 elimination) in the U.S., using the Pfizer or Moderna vaccine, is quite promising. In particular, our study shows that herd immunity can be achieved in the U.S. if at least 60% of the population are fully vaccinated. Furthermore, the prospect of eliminating the pandemic in the U.S. in the year 2021 is significantly enhanced if the vaccination program is complemented with non-pharmaceutical interventions at moderate increased levels of compliance (in relation to their baseline compliance). The study further suggests that, while the waning of natural and vaccine-derived immunity against COVID-19 induces only a marginal increase in the burden and projected time-to-elimination of the pandemic, adding the impacts of therapeutic benefits of the vaccines into the model resulted in a dramatic reduction in the burden and time-to-elimination of the pandemic.

Malaria is mainly a tropical disease and its transmission cycle is heavily influenced by environment: The life-cycles of the Anopheles mosquito vector and Plasmodium parasite are both strongly affected by ambient temperature, while suitable aquatic habitat is necessary for immature mosquito development. Therefore, how global warming may affect malaria burden is an active question, and we develop a new ordinary differential equations-based malaria transmission model that explicitly considers the temperature-dependent Anopheles gonotrophic and Plasmodium sporogonic cycles. Mosquito dynamics are coupled to infection among a human population with symptomatic and asymptomatic disease carriers, as well as temporary immunity. We also explore the effect of incorporating diurnal temperature variations upon transmission. Rigorous analysis of the model show that the non-trivial disease-free equilibrium is locally-asymptotically stable when the associated reproduction number is less than unity (this equilibrium is globally-asymptotically for a special case with no density-dependent larval and disease-induced host mortality). Numerical simulations of the model, for the case where the ambient temperature is held constant, suggest a nonlinear, hyperbolic relationship between the reproduction number and clinical malaria burden. Moreover, malaria burden peaks at 29.5 $ ^{\rm o} $ C when daily ambient temperature is held constant, but this peak decreases with increasing daily temperature variation, to about 23–25 $ ^{\rm o} $ C. Malaria burden also varies nonlinearly with temperature, such that small temperature changes influent disease mainly at marginal temperatures, suggesting that in areas where malaria is highly endemic, any response to global warming may be highly nonlinear and most typically minimal, while in areas of more marginal malaria potential (such as the East African highlands), increasing temperatures may translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium sporogonic cycle is essential, explicitly including the stages of the Anopheles gonotrophic cycle is of minimal importance.

Although pneumococcal vaccines are quite effective in reducing disease burden, factors such as imperfect vaccine efficacy and serotype replacement present an important challenge against realizing direct and herd protection benefits of the vaccines. In this study, a novel mathematical model is designed and used to describe the dynamics of two Streptococcus pneumoniae (SP) serotypes, in response to the introduction of a cohort vaccination program which targets one of the two serotypes. The model is fitted to a pediatric SP carriage prevalence data from Atlanta, GA. The model, which is rigorously analysed to investigate the existence and asymptotic stability properties of the associated equilibria (in addition to exploring conditions for competitive exclusion), is simulated to assess the impact of vaccination under different levels of serotype-specific competition and illustrate the phenomenon of serotype replacement. The calibrated model is used to forecast the carriage prevalence in the pediatric cohort over 30 years.

The large-scale use of insecticide-treated bednets (ITNs) and indoor residual spraying (IRS), over the last two decades, has resulted in a dramatic reduction of malaria incidence globally. However, the effectiveness of these interventions is now being threatened by numerous factors, such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening (when humans are not protected by the bednets). This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics. A notable feature of the model is that it stratifies the mosquito population in terms of type (wild or resistant to insecticides) and feeding preference (indoor or outdoor). The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial disease-free equilibrium, the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist). Simulations of the model, using data relevant to malaria transmission dynamics in Ethiopia (a malaria-endemic nation), show that the use of optimal ITNs alone, or in combination with optimal IRS, is more effective than the singular implementation of an optimal IRS-only strategy. Further, when the effect of the fitness cost of insecticide resistance with respect to fecundity (i.e., assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes) is accounted for, numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease, and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community. Keywords: Malaria, Insecticide resistance, ITNs, IRS, Equilibria

A new deterministic model is designed and used to gain insight into the effect of seasonal variations in temperature and vector vertical transmission on the transmission dynamics of dengue disease. The model, which incorporates (among many other features) the dynamics of the immature dengue-competent mosquitoes, vertical transmission in the vector population, density-dependent larval mortality and temperature effects, is rigorously analysed and simulated using data relevant to the disease dynamics in Chiang Mai province of Thailand. The non-trivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated basic reproduction number of the model is less than unity. Numerical simulations of the model, using data relevant to the disease dynamics in the Chiang Mai province of Thailand, show that vertical transmission in the vector population has only marginal impact on the disease dynamics, and that the effect of vertical transmission is temperature-dependent (in particular, the effect of vertical transmission on the disease dynamics increases for values of the mean monthly temperature in the range [16−28]∘C, and decreases with increasing mean monthly temperature thereafter). It is further shown that dengue burden (as measured in terms of disease incidence) is maximized when the mean monthly temperature is in the range [26−28]∘C (and dengue burden decreases for mean monthly temperature values above 28∘C). Thus, this study suggests that anti-dengue control efforts should be intensified during the period when this temperature range is recorded in the Chiang Mai province (this occurs between June and August). Keywords: Dengue, Vertical transmission, Temperature, Stability, Reproduction number

Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean). This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations), the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model (ℛ0) ranges from 0.3 to 1.4, with a mean of ℛ0=0.85. Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs), the range of ℛ0 decreases to ℛ0∈[0.1,0.6], with a mean of ℛ0=0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of ℛ0) in the community. It is shown that ℛ0 is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling), may be more effective in reducing ZVL burden in the community). Further sensitivity analysis of the model ranks the sandfly removal rate (by natural death or by feeding from insecticide-treated reservoir hosts), the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with the most effect on the disease dynamics or burden (as measured in terms of the reproduction number ℛ0). Hence, this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies (that target the identified parameters).